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# Solve the trigonometric integral $\int2\left(1+\cos\left(x\right)\right)\sin\left(x\right)dx$

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##  Final answer to the problem

$-2\cos\left(x\right)-\frac{1}{2}\cos\left(2x\right)+C_0$
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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 $2\left(1+\cos\left(x\right)\right)\sin\left(x\right)$ into $2\sin\left(x\right)+2\cos\left(x\right)\sin\left(x\right)$ by applying trigonometric identities

$\int\left(2\sin\left(x\right)+2\cos\left(x\right)\sin\left(x\right)\right)dx$

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

$\int\left(2\sin\left(x\right)+2\cos\left(x\right)\sin\left(x\right)\right)dx$

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric integral int(2(1+cos(x))sin(x))dx. Simplify 2\left(1+\cos\left(x\right)\right)\sin\left(x\right) into 2\sin\left(x\right)+2\cos\left(x\right)\sin\left(x\right) by applying trigonometric identities. Simplify the expression. The integral \int2\sin\left(x\right)dx results in: -2\cos\left(x\right). The integral \int\sin\left(2x\right)dx results in: -\frac{1}{2}\cos\left(2x\right).

##  Final answer to the problem

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

##  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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a
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◻/◻
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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