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Popular >

integral of-x+x^3

Solution

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

Solution

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

Solution steps

\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

Graph

Popular Examples

integral of (ax+b)^4

\int (a x + b)^{4} d x

integral of (x^2-9)2x

\int (x^{2} - 9) 2 x d x

integral of 1/(16+4x^2)

\int \frac{1}{16 + 4 x ^{2}} d x

integral of sin(x)(sec(x))^3

\int sin (x) (sec (x))^{3} d x

integral of e^{-2}sin(x/2)

\int e^{- 2} sin (\frac{x}{2}) d x

Frequently Asked Questions (FAQ)

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