What is the integral of x^8sin(x^9) ?

The integral of x^8sin(x^9) is -1/9 cos(x^9)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^8sin(x^9)

\int x^{8} sin (x^{9}) d x

- \frac{1}{9} cos (x^{9}) + C

Solution steps

\int x^{8} sin (x^{9}) d x

Apply u-substitution

: \int \frac{sin ( u )}{9} d u

= \int \frac{sin ( u )}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{9} (- cos (u))

Substitute back

u = x^{9}

= \frac{1}{9} (- cos (x^{9}))

Simplify

= - \frac{1}{9} cos (x^{9})

Add a constant to the solution

= - \frac{1}{9} cos (x^{9}) + C

\int \frac{y ^{2}}{y ^{2}} d y

\int \frac{1}{cos ( x ) sec ( x )} d x

\int + sec (6 x) tan (6 x) d x

\int sin (4 x - 3) cos (x + 5) d x

\int 6 x^{2} y + 2 x y^{2} d x

What is the integral of x^8sin(x^9) ?
The integral of x^8sin(x^9) is -1/9 cos(x^9)+C