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Popular >

integral of x^6(2-x)

Solution

\int x^{6} (2 - x) d x

Solution

\frac{2 x ^{7}}{7} - \frac{x ^{8}}{8} + C

Solution steps

\int x^{6} (2 - x) d x

Expand

x^{6} (2 - x) : 2 x^{6} - x^{7}

= \int 2 x^{6} - x^{7} 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^{6} d x - \int x^{7} d x

\int 2 x^{6} d x = \frac{2 x ^{7}}{7}

\int x^{7} d x = \frac{x ^{8}}{8}

= \frac{2 x ^{7}}{7} - \frac{x ^{8}}{8}

Add a constant to the solution

= \frac{2 x ^{7}}{7} - \frac{x ^{8}}{8} + C

Graph

Popular Examples

integral of (x^2+3)/(x^6(x^2+1))

\int \frac{x ^{2} + 3}{x ^{6} ( x ^{2} + 1 )} d x

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\int \frac{( x + 1 )}{3 x ^{2} + 6 x + 5} d x

integral of sqrt(7-2x^2)

\int 7 - 2 x^{2} d x

integral of 4sin(x)cos^3(x)

\int 4 sin (x) cos^{3} (x) d x

integral of 1/64 e^{4x}

\int \frac{1}{64} e^{4 x} d x

Frequently Asked Questions (FAQ)

What is the integral of x^6(2-x) ?
The integral of x^6(2-x) is (2x^7)/7-(x^8)/8+C