What is the integral of cos^{13}(x)sin(x) ?

The integral of cos^{13}(x)sin(x) is -(cos^{14}(x))/(14)+C

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integral of cos^{13}(x)sin(x)

\int cos^{13} (x) sin (x) d x

- \frac{cos ^{14} ( x )}{14} + C

Solution steps

\int cos^{13} (x) sin (x) d x

Apply u-substitution

: \int - u^{13} d u

= \int - u^{13} d u

Take the constant out:

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

= - \int u^{13} d u

Apply the Power Rule

: \frac{u ^{14}}{14}

= - \frac{u ^{14}}{14}

Substitute back

u = cos (x)

= - \frac{cos ^{14} ( x )}{14}

Add a constant to the solution

= - \frac{cos ^{14} ( x )}{14} + C

\frac{d}{d x} ((\frac{x + 8}{x - 8})^{5})

1 + (\frac{a}{x ^{2}})

x \to 0 lim (\frac{f ( x )}{x ^{2}})

\frac{d}{d t} (e^{- t} (a sin (t) + b cos (t)))

\int_{0}^{6} \frac{4 t}{( t - 7 ) ^{2}} d t

What is the integral of cos^{13}(x)sin(x) ?
The integral of cos^{13}(x)sin(x) is -(cos^{14}(x))/(14)+C