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Popular >

integral of x^6-x

Solution

\int x^{6} - x d x

Solution

\frac{x ^{7}}{7} - \frac{x ^{2}}{2} + C

Solution steps

\int x^{6} - 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^{6} d x - \int x d x

\int x^{6} d x = \frac{x ^{7}}{7}

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

= \frac{x ^{7}}{7} - \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{7}}{7} - \frac{x ^{2}}{2} + C

Popular Examples

integral of e^{-3000x}

\int e^{- 3000 x} d x

integral of (7-5x)^8

\int (7 - 5 x)^{8} d x

integral of ((2x-1))/((x-1)(x-2)(x-3))

\int \frac{( 2 x - 1 )}{( x - 1 ) ( x - 2 ) ( x - 3 )} d x

integral of (z^2+4)^4z

\int (z^{2} + 4)^{4} z d z

integral of (600x)/(sqrt(x^2+49))

\int \frac{600 x}{x ^{2} + 49} d x

Frequently Asked Questions (FAQ)

What is the integral of x^6-x ?
The integral of x^6-x is (x^7)/7-(x^2)/2+C