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Math Problems
Calculus
Evaluate definite integrals using the chain rule
What is the integral of the function
f
(
x
)
=
sin
(
2
x
)
f(x) = \sin(2x)
f
(
x
)
=
sin
(
2
x
)
?
\newline
−
1
2
cos
(
x
)
+
C
\frac{-1}{2}\cos(x) + C
2
−
1
cos
(
x
)
+
C
\newline
1
2
sin
(
x
)
+
C
\frac{1}{2}\sin(x) + C
2
1
sin
(
x
)
+
C
\newline
−
1
2
cos
(
2
x
)
+
C
\frac{-1}{2}\cos(2x) + C
2
−
1
cos
(
2
x
)
+
C
\newline
1
2
sin
(
2
x
)
+
C
\frac{1}{2}\sin(2x) + C
2
1
sin
(
2
x
)
+
C
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What is the integral of the function
f
(
x
)
=
s
i
n
(
2
x
)
\ f(x) = sin(2x)
f
(
x
)
=
s
in
(
2
x
)
?
\newline
−
1
2
cos
(
x
)
+
C
\frac{-1}{2}\cos(x) + C
2
−
1
cos
(
x
)
+
C
\newline
1
2
sin
(
x
)
+
C
\frac{1}{2} \sin(x) + C
2
1
sin
(
x
)
+
C
\newline
−
1
2
cos
(
2
x
)
+
C
\frac{-1}{2}\cos(2x) + C
2
−
1
cos
(
2
x
)
+
C
\newline
1
2
sin
(
2
x
)
+
c
\frac{1}{2} \sin(2x) + c
2
1
sin
(
2
x
)
+
c
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(
1
×
(
(
1
2
)
n
−
1
)
)
/
(
(
1
2
)
−
1
)
\left(1\times\left(\left(\frac{1}{2}\right)^n-1\right)\right)\bigg/\left(\left(\frac{1}{2}\right)-1\right)
(
1
×
(
(
2
1
)
n
−
1
)
)
/
(
(
2
1
)
−
1
)
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Solve
∫
1
(
x
−
2
)
(
x
2
+
x
+
1
)
d
x
\int \frac{1}{(x-2)(x^{2}+x+1)}\,dx
∫
(
x
−
2
)
(
x
2
+
x
+
1
)
1
d
x
.
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Simplify the expression:
1
×
(
(
1
2
)
n
−
1
)
(
1
2
−
1
)
\frac{1\times\left(\left(\frac{1}{2}\right)^n-1\right)}{\left(\frac{1}{2}-1\right)}
(
2
1
−
1
)
1
×
(
(
2
1
)
n
−
1
)
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∫
sin
(
8
x
)
d
x
9
+
sin
4
(
4
x
)
\int \frac{\sin(8x)\,dx}{9+\sin^{4}(4x)}
∫
9
+
sin
4
(
4
x
)
sin
(
8
x
)
d
x
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Evaluate the summation below.
\newline
∑
k
=
1
4
(
−
1
−
k
2
)
\sum_{k=1}^{4}\left(-1-k^{2}\right)
k
=
1
∑
4
(
−
1
−
k
2
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
n
=
0
5
(
−
2
n
2
−
n
)
\sum_{n=0}^{5}\left(-2 n^{2}-n\right)
n
=
0
∑
5
(
−
2
n
2
−
n
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
t
=
1
4
(
−
t
2
−
3
)
\sum_{t=1}^{4}\left(-t^{2}-3\right)
t
=
1
∑
4
(
−
t
2
−
3
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
n
=
1
4
(
2
−
4
n
2
)
\sum_{n=1}^{4}\left(2-4 n^{2}\right)
n
=
1
∑
4
(
2
−
4
n
2
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
k
=
2
5
(
−
4
k
+
2
k
2
)
\sum_{k=2}^{5}\left(-4 k+2 k^{2}\right)
k
=
2
∑
5
(
−
4
k
+
2
k
2
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
t
=
0
3
(
−
5
−
9
t
2
)
\sum_{t=0}^{3}\left(-5-9 t^{2}\right)
t
=
0
∑
3
(
−
5
−
9
t
2
)
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
25
10
(
0.97
)
n
−
1
\sum_{n=1}^{25} 10(0.97)^{n-1}
n
=
1
∑
25
10
(
0.97
)
n
−
1
\newline
Answer:
Get tutor help
Evaluate:
\newline
∑
n
=
0
4
(
4
x
+
n
)
\sum_{n=0}^{4}(4 x+n)
n
=
0
∑
4
(
4
x
+
n
)
\newline
Answer:
Get tutor help
Evaluate:
\newline
∑
n
=
1
4
(
n
x
−
1
)
\sum_{n=1}^{4}(n x-1)
n
=
1
∑
4
(
n
x
−
1
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
0
4
(
−
5
x
−
5
n
)
\sum_{n=0}^{4}(-5 x-5 n)
n
=
0
∑
4
(
−
5
x
−
5
n
)
\newline
Answer:
Get tutor help
Evaluate:
\newline
∑
n
=
1
5
(
−
3
x
−
4
n
)
\sum_{n=1}^{5}(-3 x-4 n)
n
=
1
∑
5
(
−
3
x
−
4
n
)
\newline
Answer:
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Evaluate the summation below.
\newline
2
∑
t
=
0
3
(
4
t
+
t
2
)
2 \sum_{t=0}^{3}\left(4 t+t^{2}\right)
2
t
=
0
∑
3
(
4
t
+
t
2
)
\newline
Answer:
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Evaluate the summation below.
\newline
∑
d
=
1
4
(
2
d
2
−
9
)
\sum_{d=1}^{4}\left(2 d^{2}-9\right)
d
=
1
∑
4
(
2
d
2
−
9
)
\newline
Answer:
Get tutor help
Evaluate the summation below.
\newline
∑
n
=
1
4
(
−
2
n
−
4
n
2
)
\sum_{n=1}^{4}\left(-2 n-4 n^{2}\right)
n
=
1
∑
4
(
−
2
n
−
4
n
2
)
\newline
Answer:
Get tutor help
Evaluate the summation below.
\newline
∑
i
=
0
3
(
−
i
2
−
5
i
)
\sum_{i=0}^{3}\left(-i^{2}-5 i\right)
i
=
0
∑
3
(
−
i
2
−
5
i
)
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
28
500
(
0.9
)
n
\sum_{n=1}^{28} 500(0.9)^{n}
n
=
1
∑
28
500
(
0.9
)
n
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
21
100
(
0.96
)
n
−
1
\sum_{n=1}^{21} 100(0.96)^{n-1}
n
=
1
∑
21
100
(
0.96
)
n
−
1
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
86
20
(
1.02
)
n
\sum_{n=1}^{86} 20(1.02)^{n}
n
=
1
∑
86
20
(
1.02
)
n
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
2
22
40
(
1.2
)
n
−
1
\sum_{n=2}^{22} 40(1.2)^{n-1}
n
=
2
∑
22
40
(
1.2
)
n
−
1
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
0
31
40
(
1.02
)
n
\sum_{n=0}^{31} 40(1.02)^{n}
n
=
0
∑
31
40
(
1.02
)
n
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
62
40
(
1.03
)
n
\sum_{n=1}^{62} 40(1.03)^{n}
n
=
1
∑
62
40
(
1.03
)
n
\newline
Answer:
Get tutor help
Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
1
28
100
(
1.07
)
n
\sum_{n=1}^{28} 100(1.07)^{n}
n
=
1
∑
28
100
(
1.07
)
n
\newline
Answer:
Get tutor help
∫
cos
3
x
d
x
sin
2
x
−
4
\int \frac{\cos ^{3} x d x}{\sin ^{2} x-4}
∫
s
i
n
2
x
−
4
c
o
s
3
x
d
x
Get tutor help
∫
0
1
3
×
2
+
x
2
+
(
4
x
−
16
)
d
x
x
2
+
3
x
+
2
3
\int_{0}^{1} \frac{3 \times 2+x^{2}+(4 x-16) d x}{\sqrt[3]{x^{2}+3 x+2}}
∫
0
1
3
x
2
+
3
x
+
2
3
×
2
+
x
2
+
(
4
x
−
16
)
d
x
Get tutor help
I
=
∫
0
π
d
x
1
+
sin
(
x
)
cos
(
x
)
I=\int_{0}^{\pi} \frac{d x}{1+\sin (x)^{\cos (x)}}
I
=
∫
0
π
1
+
s
i
n
(
x
)
c
o
s
(
x
)
d
x
Get tutor help
∫
x
2
−
x
−
21
2
x
3
−
x
2
+
8
x
−
4
d
x
\int\frac{x^{2}-x-21}{2x^{3}-x^{2}+8x-4}\,dx
∫
2
x
3
−
x
2
+
8
x
−
4
x
2
−
x
−
21
d
x
Get tutor help
Factor completely:
\newline
16
x
2
(
x
−
10
)
−
9
(
x
−
10
)
16 x^{2}(x-10)-9(x-10)
16
x
2
(
x
−
10
)
−
9
(
x
−
10
)
\newline
Answer:
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∫
−
2
2
1
+
x
2
1
+
2
x
d
x
\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x
∫
−
2
2
1
+
2
x
1
+
x
2
d
x
Get tutor help
lim
x
→
π
4
sin
(
2
x
)
−
1
sin
2
(
2
x
)
−
1
\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin (2 x)-1}{\sin ^{2}(2 x)-1}
lim
x
→
4
π
s
i
n
2
(
2
x
)
−
1
s
i
n
(
2
x
)
−
1
Get tutor help
∫
1
9
−
4
x
2
d
x
\int \frac{1}{\sqrt{9-4 x^{2}}} d x
∫
9
−
4
x
2
1
d
x
Get tutor help
∫
0
π
sin
x
d
x
\int_{0}^{\pi} \sin x d x
∫
0
π
sin
x
d
x
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27
27
27
.
∫
0
4
∣
x
2
−
9
∣
d
x
\int_{0}^{4}\left|x^{2}-9\right| d x
∫
0
4
∣
∣
x
2
−
9
∣
∣
d
x
Get tutor help
15
15
15
.
∫
1
2
(
3
x
2
−
1
)
d
x
\int_{1}^{2}\left(\frac{3}{x^{2}}-1\right) d x
∫
1
2
(
x
2
3
−
1
)
d
x
Get tutor help
∫
−
1
0
(
2
x
−
1
)
d
x
\int_{-1}^{0}(2 x-1) d x
∫
−
1
0
(
2
x
−
1
)
d
x
Get tutor help
Solve the Definite integral
\newline
∫
2
3
[
8
x
3
+
3
x
2
+
6
x
]
\int_{2}^{3}\left[8 x^{3}+3 x^{2}+6 x\right]
∫
2
3
[
8
x
3
+
3
x
2
+
6
x
]
Get tutor help
∫
0
2
π
d
x
e
sin
x
+
1
\int_{0}^{2 \pi} \frac{d x}{e^{\sin x}+1}
∫
0
2
π
e
s
i
n
x
+
1
d
x
Get tutor help
∫
0
π
4
sin
3
(
x
)
⋅
cos
(
x
)
d
x
\int_{0}^{\frac{\pi}{4}} \sin ^{3}(x) \cdot \cos (x) d x
∫
0
4
π
sin
3
(
x
)
⋅
cos
(
x
)
d
x
Get tutor help
∫
0
π
4
sin
3
(
x
)
cos
(
x
)
d
x
\int_{0}^{\frac{\pi}{4}} \sin ^{3}(x) \cos (x) d x
∫
0
4
π
sin
3
(
x
)
cos
(
x
)
d
x
Get tutor help
∫
4
d
x
(
x
2
−
2
x
+
5
)
2
\int \frac{4\,dx}{(x^{2}-2x+5)^{2}}
∫
(
x
2
−
2
x
+
5
)
2
4
d
x
Get tutor help
∫
1
3
(
1
ln
(
x
)
)
/
x
d
x
\int_{1}^{3}\left(1^{\ln(x)}\right)/x\,dx
∫
1
3
(
1
l
n
(
x
)
)
/
x
d
x
Get tutor help
∫
1
3
(
7
ln
(
x
)
x
)
d
x
\int_{1}^{3}\left(\frac{7^{\ln(x)}}{x}\right)dx
∫
1
3
(
x
7
l
n
(
x
)
)
d
x
Get tutor help
∫
(
(
1
−
3
x
)
2
x
d
x
\int(\frac{(1-\sqrt{3x})^{2}}{x} dx
∫
(
x
(
1
−
3
x
)
2
d
x
Get tutor help
Evaluate the integral.
\newline
∫
0
7
π
4
tan
(
x
7
)
d
x
\int_{0}^{\frac{7\pi}{4}} \tan \left( \frac{x}{7} \right) dx
∫
0
4
7
π
tan
(
7
x
)
d
x
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Integrate
∫
1
x
4
x
2
−
4
d
x
\int \frac{1}{x^{4}\sqrt{x^{2}-4}}\,dx
∫
x
4
x
2
−
4
1
d
x
Get tutor help
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