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Solve the trigonometric integral $\int\cos\left(x\right)\sin\left(x\right)^2dx$

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 Final answer to the problem

$\frac{1}{3}\sin\left(x\right)+\frac{-\cos\left(x\right)^{2}\sin\left(x\right)}{3}+C_0$
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 Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Simplify $\cos\left(x\right)\sin\left(x\right)^2$ into $\cos\left(x\right)-\cos\left(x\right)^{3}$ by applying trigonometric identities

$\int\left(\cos\left(x\right)-\cos\left(x\right)^{3}\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int\left(\cos\left(x\right)-\cos\left(x\right)^{3}\right)dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(cos(x)sin(x)^2)dx. Simplify \cos\left(x\right)\sin\left(x\right)^2 into \cos\left(x\right)-\cos\left(x\right)^{3} by applying trigonometric identities. Expand the integral \int\left(\cos\left(x\right)-\cos\left(x\right)^{3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\cos\left(x\right)dx results in: \sin\left(x\right). The integral \int-\cos\left(x\right)^{3}dx results in: \frac{-\cos\left(x\right)^{2}\sin\left(x\right)}{3}-\frac{2}{3}\sin\left(x\right).

 Final answer to the problem

$\frac{1}{3}\sin\left(x\right)+\frac{-\cos\left(x\right)^{2}\sin\left(x\right)}{3}+C_0$

 Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

 Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.