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Math Problems
Calculus
Find indefinite integrals using the substitution and by parts
Evaluate the integral and express your answer in simplest form.
\newline
∫
9
x
x
2
−
1
d
x
\int \frac{9}{x \sqrt{x^{2}-1}} d x
∫
x
x
2
−
1
9
d
x
\newline
Answer:
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Evaluate the integral and express your answer in simplest form.
\newline
∫
3
x
x
2
−
9
d
x
\int \frac{3}{x \sqrt{x^{2}-9}} d x
∫
x
x
2
−
9
3
d
x
\newline
Answer:
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Evaluate the integral and express your answer in simplest form.
\newline
∫
−
2
x
x
2
−
9
d
x
\int \frac{-2}{x \sqrt{x^{2}-9}} d x
∫
x
x
2
−
9
−
2
d
x
\newline
Answer:
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Evaluate the integral and express your answer in simplest form.
\newline
∫
6
4
−
x
2
d
x
\int \frac{6}{\sqrt{4-x^{2}}} d x
∫
4
−
x
2
6
d
x
\newline
Answer:
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Evaluate
∫
0
4
(
3
e
−
0.25
x
+
8
)
d
x
\int_{0}^{4}\left(3 e^{-0.25 x}+8\right) d x
∫
0
4
(
3
e
−
0.25
x
+
8
)
d
x
and express the answer in simplest form.
\newline
Answer:
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Evaluate
∫
0
6
(
10
e
−
0.5
x
+
4
)
d
x
\int_{0}^{6}\left(10 e^{-0.5 x}+4\right) d x
∫
0
6
(
10
e
−
0.5
x
+
4
)
d
x
and express the answer in simplest form.
\newline
Answer:
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Evaluate the integral and express your answer in simplest form.
\newline
∫
1
x
x
2
−
25
d
x
\int \frac{1}{x \sqrt{x^{2}-25}} d x
∫
x
x
2
−
25
1
d
x
\newline
Answer:
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Evaluate the integral and express your answer in simplest form.
\newline
∫
3
x
x
2
−
36
d
x
\int \frac{3}{x \sqrt{x^{2}-36}} d x
∫
x
x
2
−
36
3
d
x
\newline
Answer:
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∫
cot
x
9
sin
2
x
−
1
d
x
\int \frac{\cot x}{\sqrt{9\sin^{2}x-1}} \, dx
∫
9
s
i
n
2
x
−
1
c
o
t
x
d
x
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Calculate the integral and write the answer in simplest form.
\newline
∫
(
5
x
+
1
)
d
x
\int(5 x+1) d x
∫
(
5
x
+
1
)
d
x
\newline
Answer:
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Calculate the integral and write the answer in simplest form.
\newline
∫
(
−
x
−
3
−
6
)
d
x
\int\left(-x^{-3}-6\right) d x
∫
(
−
x
−
3
−
6
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
x
(
x
−
4
)
(
2
x
+
5
)
d
x
\int x(x-4)(2 x+5) \mathrm{d} x
∫
x
(
x
−
4
)
(
2
x
+
5
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
x
2
(
2
x
−
5
)
2
d
x
\int x^{2}(2 x-5)^{2} \mathrm{~d} x
∫
x
2
(
2
x
−
5
)
2
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
x
2
(
x
+
5
)
2
d
x
\int x^{2}(x+5)^{2} \mathrm{~d} x
∫
x
2
(
x
+
5
)
2
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
(
x
−
1
)
(
4
x
−
5
)
d
x
\int(x-1)(4 x-5) \mathrm{d} x
∫
(
x
−
1
)
(
4
x
−
5
)
d
x
\newline
Answer:
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∫
3
x
−
2
d
x
\int 3x^{-2}\,dx
∫
3
x
−
2
d
x
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∫
x
2
−
3
x
+
5
x
d
x
\int \frac{x^{2}-3x+5}{\sqrt{x}} \, dx
∫
x
x
2
−
3
x
+
5
d
x
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∫
cos
9
x
cos
12
x
d
x
\int \cos 9x \cos 12x \, dx
∫
cos
9
x
cos
12
x
d
x
Get tutor help
Evaluate the integral.
\newline
∫
2
x
sin
(
−
4
x
)
d
x
\int 2 x \sin (-4 x) d x
∫
2
x
sin
(
−
4
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
4
x
3
sin
(
4
x
)
d
x
\int 4 x^{3} \sin (4 x) d x
∫
4
x
3
sin
(
4
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
4
x
3
cos
(
−
4
x
)
d
x
\int 4 x^{3} \cos (-4 x) d x
∫
4
x
3
cos
(
−
4
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
6
x
e
−
x
d
x
\int-6 x e^{-x} d x
∫
−
6
x
e
−
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
3
x
e
−
4
x
d
x
\int 3 x e^{-4 x} d x
∫
3
x
e
−
4
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
2
x
2
e
−
x
d
x
\int 2 x^{2} e^{-x} d x
∫
2
x
2
e
−
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
4
x
2
sin
(
3
x
)
d
x
\int 4 x^{2} \sin (3 x) d x
∫
4
x
2
sin
(
3
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
2
x
2
e
4
x
d
x
\int 2 x^{2} e^{4 x} d x
∫
2
x
2
e
4
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
2
e
2
x
d
x
\int-x^{2} e^{2 x} d x
∫
−
x
2
e
2
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
2
x
2
4
−
2
x
d
x
\int 2 x^{2} 4^{-2 x} d x
∫
2
x
2
4
−
2
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
2
x
e
4
x
d
x
\int-2 x e^{4 x} d x
∫
−
2
x
e
4
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
3
x
sin
(
−
x
)
d
x
\int 3 x \sin (-x) d x
∫
3
x
sin
(
−
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
x
e
2
x
d
x
\int x e^{2 x} d x
∫
x
e
2
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
2
x
2
ln
(
4
x
)
d
x
\int-2 x^{2} \ln (4 x) d x
∫
−
2
x
2
ln
(
4
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
5
x
cos
(
5
x
+
5
)
d
x
\int-5 x \cos (5 x+5) d x
∫
−
5
x
cos
(
5
x
+
5
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
5
x
cos
(
3
x
)
d
x
\int-5 x \cos (3 x) d x
∫
−
5
x
cos
(
3
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
6
x
e
x
+
2
d
x
\int 6 x e^{x+2} d x
∫
6
x
e
x
+
2
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
4
x
ln
(
6
x
)
d
x
\int-4 x \ln (6 x) d x
∫
−
4
x
ln
(
6
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
6
x
cos
(
4
x
)
d
x
\int 6 x \cos (4 x) d x
∫
6
x
cos
(
4
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
2
x
e
x
+
5
d
x
\int-2 x e^{x+5} d x
∫
−
2
x
e
x
+
5
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
4
x
−
2
ln
(
x
)
d
x
\int-4 x^{-2} \ln (x) d x
∫
−
4
x
−
2
ln
(
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
e
−
x
+
4
d
x
\int-x e^{-x+4} d x
∫
−
x
e
−
x
+
4
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
ln
(
−
2
x
)
d
x
\int-x \ln (-2 x) d x
∫
−
x
ln
(
−
2
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
2
x
e
3
x
+
2
d
x
\int-2 x e^{3 x+2} d x
∫
−
2
x
e
3
x
+
2
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
−
3
ln
(
5
x
)
d
x
\int-x^{-3} \ln (5 x) d x
∫
−
x
−
3
ln
(
5
x
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
4
x
2
ln
(
−
4
x
)
d
x
\int 4 x^{2} \ln (-4 x) d x
∫
4
x
2
ln
(
−
4
x
)
d
x
\newline
Answer:
Get tutor help
Evaluate the integral.
\newline
∫
2
x
2
ln
(
−
3
x
)
d
x
\int 2 x^{2} \ln (-3 x) d x
∫
2
x
2
ln
(
−
3
x
)
d
x
\newline
Answer:
Get tutor help
Evaluate the integral.
\newline
∫
5
x
e
3
x
d
x
\int 5 x e^{3 x} d x
∫
5
x
e
3
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
cos
(
−
2
x
+
6
)
d
x
\int-x \cos (-2 x+6) d x
∫
−
x
cos
(
−
2
x
+
6
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
x
e
−
2
x
d
x
\int-x e^{-2 x} d x
∫
−
x
e
−
2
x
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
3
x
cos
(
−
2
x
+
2
)
d
x
\int 3 x \cos (-2 x+2) d x
∫
3
x
cos
(
−
2
x
+
2
)
d
x
\newline
Answer:
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Evaluate the integral.
\newline
∫
−
6
x
sin
(
−
x
)
d
x
\int-6 x \sin (-x) d x
∫
−
6
x
sin
(
−
x
)
d
x
\newline
Answer:
Get tutor help
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