What is the integral of 6xsqrt(3x^2+2) ?

The integral of 6xsqrt(3x^2+2) is 2/3 (3x^2+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 6xsqrt(3x^2+2)

\int 6 x 3 x^{2} + 2 d x

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

Solution steps

\int 6 x 3 x^{2} + 2 d x

Take the constant out:

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

= 6 \cdot \int x 3 x^{2} + 2 d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 3 x^{2} + 2

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

Simplify

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

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

Add a constant to the solution

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

f (x) = x + 7

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

\frac{d}{d x} (e^{- 2 x} (1 - x))

\frac{d}{d x} (10 (3 x^{2} + 7 x - 3)^{10})

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

What is the integral of 6xsqrt(3x^2+2) ?
The integral of 6xsqrt(3x^2+2) is 2/3 (3x^2+2)^{3/2}+C