en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+y^2)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (x^2+2x-6)

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

integral of (x^3)/((2x^4+7)^2)

\int \frac{x ^{3}}{( 2 x ^{4} + 7 ) ^{2}} d x

integral of e^{5x+9}

\int e^{5 x + 9} d x

integral of xsqrt(8+x^2)

\int x 8 + x^{2} d x

integral of u/(e^u)

\int \frac{u}{e ^{u}} d u

Frequently Asked Questions (FAQ)

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