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Popular >

integral of-x+2x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of sqrt(1-6x)

\int 1 - 6 x d x

integral of (e^{arcsin(x)})/(sqrt(1-x^2))

\int \frac{e ^{a r c s i n (x)}}{1 - x ^{2}} d x

derivative of (12/(x+2)-3)

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

derivative of (x^2-4x/(x+1))

\frac{d}{d x} (\frac{x ^{2} - 4 x}{x + 1})

integral of-(x^2+11x+28)/((x+2)^2)

\int - \frac{x ^{2} + 11 x + 28}{( x + 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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