What is the integral of 2x^5+7+1/(x^3) ?

The integral of 2x^5+7+1/(x^3) is (x^6)/3+7x-1/(2x^2)+C

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integral of 2x^5+7+1/(x^3)

\int 2 x^{5} + 7 + \frac{1}{x ^{3}} d x

\frac{x ^{6}}{3} + 7 x - \frac{1}{2 x ^{2}} + C

Solution steps

\int 2 x^{5} + 7 + \frac{1}{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 2 x^{5} d x + \int 7 d x + \int \frac{1}{x ^{3}} d x

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int 7 d x = 7 x

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

= \frac{x ^{6}}{3} + 7 x - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{6}}{3} + 7 x - \frac{1}{2 x ^{2}} + C

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What is the integral of 2x^5+7+1/(x^3) ?
The integral of 2x^5+7+1/(x^3) is (x^6)/3+7x-1/(2x^2)+C