en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x^3+x

Solution

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

Solution

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

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

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

Add a constant to the solution

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

Popular Examples

tangent of f(x)=2x^2+5x-3,\at x=1 tangent of

f (x) = 2 x^{2} + 5 x - 3, at x = 1

integral of (sin(2x))/(41+cos^2(x))

\int \frac{sin ( 2 x )}{41 + cos ^{2} ( x )} d x

integral from 1 to 3 of sqrt(x)ln(x)

\int_{1}^{3} x ln (x) d x

(\partial)/(\partial y)(pixsqrt(x^2+y^2))

\frac{\partial}{\partial y} (π x x^{2} + y^{2})

tangent of (-1)/((2x+1)sqrt(2x+1))tangent of

\frac{- 1}{( 2 x + 1 ) 2 x + 1}

Frequently Asked Questions (FAQ)

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