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

The integral of x^2(1+x^3) is (x^3)/3+(x^6)/6+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(1+x^3)

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

\frac{x ^{3}}{3} + \frac{x ^{6}}{6} + C

Solution steps

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

Expand

x^{2} (1 + x^{3}) : x^{2} + x^{5}

= \int x^{2} + x^{5} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x + \int x^{5} d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int x^{5} d x = \frac{x ^{6}}{6}

= \frac{x ^{3}}{3} + \frac{x ^{6}}{6}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{6}}{6} + C

\int \frac{4}{3} t^{3} - 4 t^{2} + 3 t + 10 d t

\frac{d}{d t} (t + 1)

x \to 5 + lim (\frac{2}{x ^{2} - 25})

cos (a^{8} + x^{8})

x \to 0 lim (\frac{x + 36 - 6}{x})

What is the integral of x^2(1+x^3) ?
The integral of x^2(1+x^3) is (x^3)/3+(x^6)/6+C