What is the integral of (8x+5)sqrt(4x^2+5x) ?

The integral of (8x+5)sqrt(4x^2+5x) is 2/3 (4x^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 (8x+5)sqrt(4x^2+5x)

\int (8 x + 5) 4 x^{2} + 5 x d x

\frac{2}{3} (4 x^{2} + 5 x)^{\frac{3}{2}} + C

Solution steps

\int (8 x + 5) 4 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 = 4 x^{2} + 5 x

= \frac{2}{3} (4 x^{2} + 5 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (4 x^{2} + 5 x)^{\frac{3}{2}} + C

- \frac{1}{x ^{2}}, 2

y^{^{'}} = 0

\int \frac{x}{6} + π d x

(\frac{x ^{2} - x ^{4}}{8})^{^{'}}

What is the integral of (8x+5)sqrt(4x^2+5x) ?
The integral of (8x+5)sqrt(4x^2+5x) is 2/3 (4x^2+5x)^{3/2}+C