What is the integral of 1/(x^3)+6/(x^7) ?

The integral of 1/(x^3)+6/(x^7) is -1/(2x^2)-1/(x^6)+C

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integral of 1/(x^3)+6/(x^7)

\int \frac{1}{x ^{3}} + \frac{6}{x ^{7}} d x

- \frac{1}{2 x ^{2}} - \frac{1}{x ^{6}} + C

Solution steps

\int \frac{1}{x ^{3}} + \frac{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 \frac{1}{x ^{3}} d x + \int \frac{6}{x ^{7}} d x

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

\int \frac{6}{x ^{7}} d x = - \frac{1}{x ^{6}}

= - \frac{1}{2 x ^{2}} - \frac{1}{x ^{6}}

Add a constant to the solution

= - \frac{1}{2 x ^{2}} - \frac{1}{x ^{6}} + C

n = 0 \sum \infty \frac{1}{( 2 + 2 n ) ^{3}}

\int_{- 1}^{3} 2 x^{2} + 8 d x

\int 4 y^{5} d y

x (x - 8)

f (x) = 2 x^{3} - x^{2} + 2, at x = 2

What is the integral of 1/(x^3)+6/(x^7) ?
The integral of 1/(x^3)+6/(x^7) is -1/(2x^2)-1/(x^6)+C