What is the integral of x^2sqrt(x^3+11) ?

The integral of x^2sqrt(x^3+11) is 2/9 (x^3+11)^{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 x^2sqrt(x^3+11)

\int x^{2} x^{3} + 11 d x

\frac{2}{9} (x^{3} + 11)^{\frac{3}{2}} + C

Solution steps

\int x^{2} x^{3} + 11 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 = x^{3} + 11

= \frac{1}{3} \cdot \frac{2}{3} (x^{3} + 11)^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} (x^{3} + 11)^{\frac{3}{2}} : \frac{2}{9} (x^{3} + 11)^{\frac{3}{2}}

= \frac{2}{9} (x^{3} + 11)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (x^{3} + 11)^{\frac{3}{2}} + C

y = x^{2} - (sin (x))^{2}

\int (1 + ln (x)) d x

2 y^{^{''}} + 7 y^{^{'}} + 3 y = 6, y (0) = 0, y^{^{'}} (0) = 0

f (x) = \frac{2}{x + 7}

\int x cos (3) x^{2} d x

What is the integral of x^2sqrt(x^3+11) ?
The integral of x^2sqrt(x^3+11) is 2/9 (x^3+11)^{3/2}+C