en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(1+x^2)

Solution

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

Solution

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

Solution steps

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

Expand

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

= \int x + x^{3} 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 d x + \int x^{3} d x

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of x^3-12x^2+45x

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x)

limit as x approaches 2 of (-2)/0

x \to 2 lim (\frac{- 2}{0})

11x-4ysqrt(x^2+1)y^'=0,y(0)=2

11 x - 4 y x^{2} + 1 y^{^{'}} = 0, y (0) = 2

derivative of e^{x/2} 1/2

\frac{d}{d x} (e^{\frac{x}{2}} \frac{1}{2})

derivative of y=x^2sin^4(x)+xcos^{-6}(x)derivative of

y = x^{2} sin^{4} (x) + x cos^{- 6} (x)

Frequently Asked Questions (FAQ)

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