What is the integral of sin(x)(1+cos(x))^4 ?

The integral of sin(x)(1+cos(x))^4 is -((1+cos(x))^5)/5+C

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integral of sin(x)(1+cos(x))^4

\int sin (x) (1 + cos (x))^{4} d x

- \frac{( 1 + cos ( x ) ) ^{5}}{5} + C

Solution steps

\int sin (x) (1 + cos (x))^{4} d x

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

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

= - \int u^{4} d u

Apply the Power Rule

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

= - \frac{u ^{5}}{5}

Substitute back

u = 1 + cos (x)

= - \frac{( 1 + cos ( x ) ) ^{5}}{5}

Add a constant to the solution

= - \frac{( 1 + cos ( x ) ) ^{5}}{5} + C

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

e^{- t} (\frac{e ^{t} + e ^{- t}}{2})

f (x) = \frac{25 x ^{3}}{3} + 10 x^{2} + 4 x - 7

n \to \infty lim (4 n)

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}} y^{\frac{1}{3}})

What is the integral of sin(x)(1+cos(x))^4 ?
The integral of sin(x)(1+cos(x))^4 is -((1+cos(x))^5)/5+C