What is the integral of x^{17}sin(x^{18}) ?

The integral of x^{17}sin(x^{18}) is -1/18 cos(x^{18})+C

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integral of x^{17}sin(x^{18})

\int x^{17} sin (x^{18}) d x

- \frac{1}{18} cos (x^{18}) + C

Solution steps

\int x^{17} sin (x^{18}) d x

Apply u-substitution

: \int \frac{sin ( u )}{18} d u

= \int \frac{sin ( u )}{18} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{18} (- cos (u))

Substitute back

u = x^{18}

= \frac{1}{18} (- cos (x^{18}))

Simplify

= - \frac{1}{18} cos (x^{18})

Add a constant to the solution

= - \frac{1}{18} cos (x^{18}) + C

g (t) = \frac{1 - 3 t}{4 + t}

f (x) = \frac{1}{x ^{3} + 2 x ^{2} - 1}

\int (e^{- \frac{x}{4}} + e^{\frac{x}{2}}) d x

(x + 1) \frac{d y}{d x} = (x + 6)

x \to 3 lim (\frac{x}{2} + 1)

What is the integral of x^{17}sin(x^{18}) ?
The integral of x^{17}sin(x^{18}) is -1/18 cos(x^{18})+C