What is the integral of (14x+5)sqrt(7x^2+5x) ?

The integral of (14x+5)sqrt(7x^2+5x) is 2/3 (7x^2+5x)^{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 (14x+5)sqrt(7x^2+5x)

\int (14 x + 5) 7 x^{2} + 5 x d x

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

Solution steps

\int (14 x + 5) 7 x^{2} + 5 x d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = 7 x^{2} + 5 x

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

Add a constant to the solution

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

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

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

3 x (y^{2} + 1) d x + y (x^{2} + 2) d y = 0

y^{^{'}} = \frac{x - 1}{y - 4}

\frac{\partial}{\partial y} (3 y^{2} + 3 x^{2} - 12 y)

What is the integral of (14x+5)sqrt(7x^2+5x) ?
The integral of (14x+5)sqrt(7x^2+5x) is 2/3 (7x^2+5x)^{3/2}+C