What is the integral of (3x^2)/(sqrt(2x^3+9)) ?

The integral of (3x^2)/(sqrt(2x^3+9)) is sqrt(2x^3+9)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x^2)/(sqrt(2x^3+9))

\int \frac{3 x ^{2}}{2 x ^{3} + 9} d x

2 x^{3} + 9 + C

Solution steps

\int \frac{3 x ^{2}}{2 x ^{3} + 9} d x

Take the constant out:

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

= 3 \cdot \int \frac{x ^{2}}{2 x ^{3} + 9} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= 3 \cdot \int \frac{1}{6 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{6} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 3 \cdot \frac{1}{6} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 x^{3} + 9

= 3 \cdot \frac{1}{6} \cdot 2 (2 x^{3} + 9)^{\frac{1}{2}}

Simplify

3 \cdot \frac{1}{6} \cdot 2 (2 x^{3} + 9)^{\frac{1}{2}} : 2 x^{3} + 9

= 2 x^{3} + 9

Add a constant to the solution

= 2 x^{3} + 9 + C

\int \frac{2 x - 1}{3} d x

\int sin (3 x) cos^{3} (3 x) d x

\int \frac{x}{x ^{2} + 2 x + 4} d x

\int \frac{2000}{400 x} d x

\int sin^{5} (x) cos^{10} (x) d x

What is the integral of (3x^2)/(sqrt(2x^3+9)) ?
The integral of (3x^2)/(sqrt(2x^3+9)) is sqrt(2x^3+9)+C