What is the integral of x^6sin(x^7) ?

The integral of x^6sin(x^7) is -1/7 cos(x^7)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^6sin(x^7)

\int x^{6} sin (x^{7}) d x

- \frac{1}{7} cos (x^{7}) + C

Solution steps

\int x^{6} sin (x^{7}) d x

Apply u-substitution

: \int \frac{sin ( u )}{7} d u

= \int \frac{sin ( u )}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{7} (- cos (u))

Substitute back

u = x^{7}

= \frac{1}{7} (- cos (x^{7}))

Simplify

= - \frac{1}{7} cos (x^{7})

Add a constant to the solution

= - \frac{1}{7} cos (x^{7}) + C

\int 15 sec^{2} (x) tan^{4} (x) d x

\int (x^{2} + 1)^{5} x d x

\int 3 x^{2} + 8 d x

\int 3 x^{2} + 9 d x

\int x (x + 9)^{7} d x

What is the integral of x^6sin(x^7) ?
The integral of x^6sin(x^7) is -1/7 cos(x^7)+C