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Popular >

integral of 2x-2x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (7x^3)/(4sqrt(x^6))

\int \frac{7 x ^{3}}{4 x ^{6}} d x

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\int \frac{ln ( x ^{13} )}{x} d x

integral of ((3x-7x^2))/x

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

Frequently Asked Questions (FAQ)

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