What is the integral of sin(x)(2cos(x)) ?

The integral of sin(x)(2cos(x)) is sin^2(x)+C

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integral of sin(x)(2cos(x))

\int sin (x) (2 cos (x)) d x

sin^{2} (x) + C

Solution steps

\int sin (x) \cdot 2 cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sin (x) cos (x) d x

Apply u-substitution

= 2 \cdot \int u d u

Apply the Power Rule

= 2 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 2 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

2 \cdot \frac{sin ^{2} ( x )}{2} : sin^{2} (x)

= sin^{2} (x)

Add a constant to the solution

= sin^{2} (x) + C

What is the integral of sin(x)(2cos(x)) ?
The integral of sin(x)(2cos(x)) is sin^2(x)+C