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

The integral of x^2(x^3+2)^3 is 1/12 (x^3+2)^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{12} (x^{3} + 2)^{4} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{3} \cdot \frac{u ^{4}}{4}

Substitute back

u = x^{3} + 2

= \frac{1}{3} \cdot \frac{( x ^{3} + 2 ) ^{4}}{4}

Simplify

\frac{1}{3} \cdot \frac{( x ^{3} + 2 ) ^{4}}{4} : \frac{1}{12} (x^{3} + 2)^{4}

= \frac{1}{12} (x^{3} + 2)^{4}

Add a constant to the solution

= \frac{1}{12} (x^{3} + 2)^{4} + C

\int \frac{1}{s ^{2} - 1} d s

\int e^{x \cdot x} d x

\int e^{\frac{a}{x}} d x

\int (3 x^{2} - 6 x + 5) d x

\int (2 + x)^{6} d x

What is the integral of x^2(x^3+2)^3 ?
The integral of x^2(x^3+2)^3 is 1/12 (x^3+2)^4+C