What is the integral of 11xsqrt(x^2+8) ?

The integral of 11xsqrt(x^2+8) is 11/3 (x^2+8)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 11xsqrt(x^2+8)

\int 11 x x^{2} + 8 d x

\frac{11}{3} (x^{2} + 8)^{\frac{3}{2}} + C

Solution steps

\int 11 x x^{2} + 8 d x

Take the constant out:

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

= 11 \cdot \int x x^{2} + 8 d x

Apply u-substitution

: \int u^{2} d u

= 11 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 11 \cdot \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 8

= 11 \cdot \frac{( x ^{2} + 8 ) ^{3}}{3}

Simplify

11 \cdot \frac{( x ^{2} + 8 ) ^{3}}{3} : \frac{11}{3} (x^{2} + 8)^{\frac{3}{2}}

= \frac{11}{3} (x^{2} + 8)^{\frac{3}{2}}

Add a constant to the solution

= \frac{11}{3} (x^{2} + 8)^{\frac{3}{2}} + C

\int 4 e^{3.5 x} d x

\int (5 sinh (x) + x^{5}) d x

\int \frac{12 + 3 e ^{2 t}}{e ^{2 t}} d t

\int - 4 \frac{1 + x}{1 - x} d x

What is the integral of 11xsqrt(x^2+8) ?
The integral of 11xsqrt(x^2+8) is 11/3 (x^2+8)^{3/2}+C