What is the integral of (5x^2+1)(sqrt(5x^3+3x-2)) ?

The integral of (5x^2+1)(sqrt(5x^3+3x-2)) is 2/9 (5x^3+3x-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 (5x^2+1)(sqrt(5x^3+3x-2))

\int (5 x^{2} + 1) (5 x^{3} + 3 x - 2) d x

\frac{2}{9} (5 x^{3} + 3 x - 2)^{\frac{3}{2}} + C

Solution steps

\int (5 x^{2} + 1) 5 x^{3} + 3 x - 2 d x

Apply u-substitution

: \int \frac{u}{3} d u

= \int \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 5 x^{3} + 3 x - 2

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

Simplify

\frac{1}{3} \cdot \frac{2}{3} (5 x^{3} + 3 x - 2)^{\frac{3}{2}} : \frac{2}{9} (5 x^{3} + 3 x - 2)^{\frac{3}{2}}

= \frac{2}{9} (5 x^{3} + 3 x - 2)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (5 x^{3} + 3 x - 2)^{\frac{3}{2}} + C

\int 4 - (x - 3)^{2} d x

\int - \frac{x}{e ^{2 x}} d x

\int (t^{2} - sin (t)) d t

\int \frac{x - 12}{x ^{2} - 4 x} d x

\int \frac{cos ( u )}{sin ( u )} d u

What is the integral of (5x^2+1)(sqrt(5x^3+3x-2)) ?
The integral of (5x^2+1)(sqrt(5x^3+3x-2)) is 2/9 (5x^3+3x-2)^{3/2}+C