What is the integral of xsqrt(5x^2+7) ?

The integral of xsqrt(5x^2+7) is 1/15 (5x^2+7)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xsqrt(5x^2+7)

\int x 5 x^{2} + 7 d x

\frac{1}{15} (5 x^{2} + 7)^{\frac{3}{2}} + C

Solution steps

\int x 5 x^{2} + 7 d x

Apply u-substitution

= \int \frac{u}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int u d u

Apply the Power Rule

= \frac{1}{10} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 5 x^{2} + 7

= \frac{1}{10} \cdot \frac{2}{3} (5 x^{2} + 7)^{\frac{3}{2}}

Simplify

\frac{1}{10} \cdot \frac{2}{3} (5 x^{2} + 7)^{\frac{3}{2}} : \frac{1}{15} (5 x^{2} + 7)^{\frac{3}{2}}

= \frac{1}{15} (5 x^{2} + 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{15} (5 x^{2} + 7)^{\frac{3}{2}} + C

What is the integral of xsqrt(5x^2+7) ?
The integral of xsqrt(5x^2+7) is 1/15 (5x^2+7)^{3/2}+C