What is the integral of 3cos(x)sin(x) ?

The integral of 3cos(x)sin(x) is 3/2 sin^2(x)+C

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integral of 3cos(x)sin(x)

\int 3 cos (x) sin (x) d x

\frac{3}{2} sin^{2} (x) + C

Solution steps

\int 3 cos (x) sin (x) d x

Take the constant out:

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

= 3 \cdot \int cos (x) sin (x) d x

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 3 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 3 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

3 \cdot \frac{sin ^{2} ( x )}{2} : \frac{3}{2} sin^{2} (x)

= \frac{3}{2} sin^{2} (x)

Add a constant to the solution

= \frac{3}{2} sin^{2} (x) + C

n = 1 \sum \infty \frac{n ^{2}}{2 ^{n}}

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\frac{\partial}{\partial x} ((2 x y) (x^{2} + y^{2}))

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What is the integral of 3cos(x)sin(x) ?
The integral of 3cos(x)sin(x) is 3/2 sin^2(x)+C