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# Solve the trigonometric integral $\int2\sin\left(x\right)\cos\left(x\right)^2dx$

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##  Final answer to the problem

$\frac{-12\sec\left(\frac{x}{2}\right)^{4}+24\tan\left(\frac{x}{2}\right)^{2}+8}{3\sec\left(\frac{x}{2}\right)^{6}}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Weierstrass Substitution
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
• FOIL Method
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1

We can solve the integral $\int2\sin\left(x\right)\cos\left(x\right)^2dx$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution

$t=\tan\left(\frac{x}{2}\right)$

Learn how to solve problems step by step online.

$t=\tan\left(\frac{x}{2}\right)$

Learn how to solve problems step by step online. Solve the trigonometric integral int(2sin(x)cos(x)^2)dx. We can solve the integral \int2\sin\left(x\right)\cos\left(x\right)^2dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.

##  Final answer to the problem

$\frac{-12\sec\left(\frac{x}{2}\right)^{4}+24\tan\left(\frac{x}{2}\right)^{2}+8}{3\sec\left(\frac{x}{2}\right)^{6}}+C_0$

##  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
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f
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n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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