What is the integral of sqrt(1+5x^2)(10x) ?

The integral of sqrt(1+5x^2)(10x) is 2/3 (1+5x^2)^{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 sqrt(1+5x^2)(10x)

\int 1 + 5 x^{2} (10 x) d x

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

Solution steps

\int 1 + 5 x^{2} \cdot 10 x d x

Take the constant out:

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

= 10 \cdot \int 1 + 5 x^{2} x d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 1 + 5 x^{2}

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

Simplify

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

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

Add a constant to the solution

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

y = 3 x^{2} + \frac{10 x}{3} - 2

\frac{d}{d x} (\frac{tan ^{3} ( x )}{3})

n = 1 \sum \infty \frac{2 n !}{n ^{5}}

\frac{\partial}{\partial x} (- 6 e^{- 3 x^{2} - y^{2}} x)

(1 - 2 x) (3 x - 4), at x = 2

What is the integral of sqrt(1+5x^2)(10x) ?
The integral of sqrt(1+5x^2)(10x) is 2/3 (1+5x^2)^{3/2}+C