What is the integral of sin^4(x/7)cos(x/7) ?

The integral of sin^4(x/7)cos(x/7) is 7/5 sin^5(x/7)+C

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integral of sin^4(x/7)cos(x/7)

\int sin^{4} (\frac{x}{7}) cos (\frac{x}{7}) d x

\frac{7}{5} sin^{5} (\frac{x}{7}) + C

Solution steps

\int sin^{4} (\frac{x}{7}) cos (\frac{x}{7}) d x

Apply u-substitution

: \int sin^{4} (u) cos (u) \cdot 7 d u

= \int sin^{4} (u) cos (u) \cdot 7 d u

Take the constant out:

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

= 7 \cdot \int sin^{4} (u) cos (u) d u

Apply u-substitution

: \int v^{4} d v

= 7 \cdot \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

= 7 \cdot \frac{v ^{5}}{5}

Substitute back

= 7 \cdot \frac{sin ^{5} ( \frac{x}{7} )}{5}

Simplify

7 \cdot \frac{sin ^{5} ( \frac{x}{7} )}{5} : \frac{7}{5} sin^{5} (\frac{x}{7})

= \frac{7}{5} sin^{5} (\frac{x}{7})

Add a constant to the solution

= \frac{7}{5} sin^{5} (\frac{x}{7}) + C

\frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2})

\frac{d}{d x} (ln (2 x))

\int cos (x) (2 + 5 sin^{2} (x)) d x

\frac{\partial}{\partial x} (x^{4} ln (zy))

\frac{d}{d x} (\frac{e ^{x}}{x ^{n}})

What is the integral of sin^4(x/7)cos(x/7) ?
The integral of sin^4(x/7)cos(x/7) is 7/5 sin^5(x/7)+C