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Popular >

integral of (x^5-5x)

Solution

\int (x^{5} - 5 x) d x

Solution

\frac{x ^{6}}{6} - \frac{5 x ^{2}}{2} + C

Solution steps

\int x^{5} - 5 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 x^{5} d x - \int 5 x d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{x ^{6}}{6} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{5 x ^{2}}{2} + C

Graph

Popular Examples

integral of x/e

\int \frac{x}{e} d x

integral of sqrt(1+x^4)x^3

\int 1 + x^{4} x^{3} d x

integral of 10sec^2(x)tan^4(x)

\int 10 sec^{2} (x) tan^{4} (x) d x

integral of (4x+1)/(x^2-6x+13)

\int \frac{4 x + 1}{x ^{2} - 6 x + 13} d x

integral of 2/(x^2+2x)

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

Frequently Asked Questions (FAQ)

What is the integral of (x^5-5x) ?
The integral of (x^5-5x) is (x^6)/6-(5x^2)/2+C