What is the integral of x^{13}sin(x^{14}) ?

The integral of x^{13}sin(x^{14}) is -1/14 cos(x^{14})+C

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integral of x^{13}sin(x^{14})

\int x^{13} sin (x^{14}) d x

- \frac{1}{14} cos (x^{14}) + C

Solution steps

\int x^{13} sin (x^{14}) d x

Apply u-substitution

: \int \frac{sin ( u )}{14} d u

= \int \frac{sin ( u )}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{14} (- cos (u))

Substitute back

u = x^{14}

= \frac{1}{14} (- cos (x^{14}))

Simplify

= - \frac{1}{14} cos (x^{14})

Add a constant to the solution

= - \frac{1}{14} cos (x^{14}) + C

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What is the integral of x^{13}sin(x^{14}) ?
The integral of x^{13}sin(x^{14}) is -1/14 cos(x^{14})+C