en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x^3+xy^2

Solution

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

Solution

\frac{x ^{4}}{4} + \frac{y ^{2} x ^{2}}{2} + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} + \frac{y ^{2} x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{y ^{2} x ^{2}}{2} + C

Graph

Popular Examples

integral of (4-7x)\sqrt[3]{x}

integral of 1/(e^m+4e^{-m)}

integral of (6x^3)/(x-1)

integral of 1/((9-16x^2)^{3/2)}

integral of (x^2)/(x^2+2x+5)

Frequently Asked Questions (FAQ)

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