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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

Popular Examples

tangent of y=x^2+5,(-5,30)tangent of

y = x^{2} + 5, (- 5, 30)

derivative of sqrt(2x)derivative of

2 x

derivative of f(x)=(x^4-4x)e^x derivative of

f (x) = (x^{4} - 4 x) e^{x}

derivative of-8/(x^9)derivative of

- \frac{8}{x ^{9}}

integral of (x^4+2x-9)ln(x)

\int (x^{4} + 2 x - 9) ln (x) 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