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

The integral of (x^2sqrt(1+x^3)) is 2/9 (1+x^3)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^2sqrt(1+x^3))

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

\frac{2}{9} (1 + x^{3})^{\frac{3}{2}} + C

Solution steps

\int x^{2} 1 + x^{3} d x

Apply u-substitution

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

Substitute back

u = 1 + x^{3}

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

Simplify

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

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

Add a constant to the solution

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

\int - \frac{1}{x ^{7}} d x

\int (5 x^{4} + 6 x - 8) d x

\int \frac{5 x + 4}{x ^{2} + 1} d x

\int 2 x (x^{2} + 11)^{5} d x

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

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