What is the integral of (8x^7+9)sqrt(x^8+9x) ?

The integral of (8x^7+9)sqrt(x^8+9x) is 2/3 (x^8+9x)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (8x^7+9)sqrt(x^8+9x)

\int (8 x^{7} + 9) x^{8} + 9 x d x

\frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}} + C

Solution steps

\int (8 x^{7} + 9) x^{8} + 9 x d x

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x^{8} + 9 x

= \frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}} + C

What is the integral of (8x^7+9)sqrt(x^8+9x) ?
The integral of (8x^7+9)sqrt(x^8+9x) is 2/3 (x^8+9x)^{3/2}+C