What is the integral of xsqrt(5x^2+1) ?

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

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

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

Solution steps

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

Apply u-substitution

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

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

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

Substitute back

u = 5 x^{2} + 1

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{e ^{- x}}{e ^{- x} + e ^{x}} d x

\int x^{2} - 2 x - 1 d x

\int \frac{csc ^{2} ( x )}{x} d x

\int \frac{10 x ^{9}}{x ^{10} + 1} d x

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