What is the integral of 3cos^2(x)sin(x) ?

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

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integral of 3cos^2(x)sin(x)

\int 3 cos^{2} (x) sin (x) d x

- cos^{3} (x) + C

Solution steps

\int 3 cos^{2} (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^{2} (x) sin (x) d x

Apply u-substitution

: \int - u^{2} d u

= 3 \cdot \int - u^{2} d u

Take the constant out:

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

= 3 (- \int u^{2} d u)

Apply the Power Rule

: \frac{u ^{3}}{3}

= 3 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= 3 (- \frac{cos ^{3} ( x )}{3})

Simplify

3 (- \frac{cos ^{3} ( x )}{3}) : - cos^{3} (x)

= - cos^{3} (x)

Add a constant to the solution

= - cos^{3} (x) + C

\int (2 t^{2} + 3)^{\frac{4}{3}} t^{3} d t

f (x) = (x^{2} + 3 x - 1) e^{x}

f (x) = - x^{2} + 5 x

- 3 lo g_{4} (x)

n \to \infty lim (\frac{( 2 n ) ^{2 n}}{( 2 n + 2 ) ^{2 n}})

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