What is the integral of 8cos^4(θ)sin(θ) ?

The integral of 8cos^4(θ)sin(θ) is -8/5 cos^5(θ)+C

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integral of 8cos^4(θ)sin(θ)

\int 8 cos^{4} (θ) sin (θ) d θ

- \frac{8}{5} cos^{5} (θ) + C

Solution steps

\int 8 cos^{4} (θ) sin (θ) d θ

Take the constant out:

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

= 8 \cdot \int cos^{4} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{4} d u

= 8 \cdot \int - u^{4} d u

Take the constant out:

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

= 8 (- \int u^{4} d u)

Apply the Power Rule

: \frac{u ^{5}}{5}

= 8 (- \frac{u ^{5}}{5})

Substitute back

u = cos (θ)

= 8 (- \frac{cos ^{5} ( θ )}{5})

Simplify

8 (- \frac{cos ^{5} ( θ )}{5}) : - \frac{8}{5} cos^{5} (θ)

= - \frac{8}{5} cos^{5} (θ)

Add a constant to the solution

= - \frac{8}{5} cos^{5} (θ) + C

\int \frac{5}{16 + x ^{2}} d x

ln (ln (8 s))

f (x) = 4 x^{4} - x^{6}

y = (6 x^{3} + 3 x + 1)^{10}

\int_{0}^{1} (x + y) d x

What is the integral of 8cos^4(θ)sin(θ) ?
The integral of 8cos^4(θ)sin(θ) is -8/5 cos^5(θ)+C