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∫
sin
2
x
sin
x
d
x
\int \frac{\sin 2 x}{\sin x} d x
∫
s
i
n
x
s
i
n
2
x
d
x
=
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Math Problems
Calculus
Find indefinite integrals using the substitution and by parts
Full solution
Q.
∫
sin
2
x
sin
x
d
x
\int \frac{\sin 2 x}{\sin x} d x
∫
s
i
n
x
s
i
n
2
x
d
x
=
Simplify using trigonometric identities:
Simplify the integral using trigonometric identities.
\newline
∫
sin
2
x
sin
x
d
x
=
∫
2
sin
x
cos
x
sin
x
d
x
=
∫
2
cos
x
d
x
\int \frac{\sin 2x}{\sin x} \, dx = \int \frac{2 \sin x \cos x}{\sin x} \, dx = \int 2 \cos x \, dx
∫
sin
x
sin
2
x
d
x
=
∫
sin
x
2
sin
x
cos
x
d
x
=
∫
2
cos
x
d
x
Integrate
2
2
2
cos x:
Integrate
2
cos
x
2 \cos x
2
cos
x
.
\newline
∫
2
cos
x
d
x
=
2
sin
x
+
C
\int 2 \cos x \, dx = 2 \sin x + C
∫
2
cos
x
d
x
=
2
sin
x
+
C
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6
x
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x
\newline
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Evaluate the integral.
\newline
∫
−
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x
sin
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−
2
x
)
d
x
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∫
−
3
x
sin
(
−
2
x
)
d
x
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