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

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

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

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

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

Solution steps

\int 2 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

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

Apply u-substitution

: \int - u^{2} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

= 2 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= 2 (- \frac{cos ^{3} ( x )}{3})

Simplify

2 (- \frac{cos ^{3} ( x )}{3}) : - \frac{2}{3} cos^{3} (x)

= - \frac{2}{3} cos^{3} (x)

Add a constant to the solution

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

\int e^{- 4 x} \cdot x d x

- \frac{3 x ^{2}}{4 y ^{2}}

2 x^{2} + 15

\frac{d}{d x} (\frac{1}{- 3 + ( 3 x + 1 ) ^{2}})

y = sec (x), (\frac{π}{6}, 2 \frac{3}{3})

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