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

The integral of xsqrt(2x^2+11) is 1/6 (2x^2+11)^{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 xsqrt(2x^2+11)

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

\frac{1}{6} (2 x^{2} + 11)^{\frac{3}{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{u}{4} d u

= \int \frac{u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 2 x^{2} + 11

= \frac{1}{4} \cdot \frac{2}{3} (2 x^{2} + 11)^{\frac{3}{2}}

Simplify

\frac{1}{4} \cdot \frac{2}{3} (2 x^{2} + 11)^{\frac{3}{2}} : \frac{1}{6} (2 x^{2} + 11)^{\frac{3}{2}}

= \frac{1}{6} (2 x^{2} + 11)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{6} (2 x^{2} + 11)^{\frac{3}{2}} + C

\int sin^{2} (x) cos^{2} (d) x d x

\int (x y e^{x z} + z^{3}) d z

\int cos (2 t) d t

\int (x^{3} - \frac{1}{x ^{2}})^{2} d x

\int x^{2} - 7 x + 12 d x

What is the integral of xsqrt(2x^2+11) ?
The integral of xsqrt(2x^2+11) is 1/6 (2x^2+11)^{3/2}+C