What is the integral of 3sqrt(x)+(10)/(x^6) ?

The integral of 3sqrt(x)+(10)/(x^6) is 2x^{3/2}-2/(x^5)+C

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integral of 3sqrt(x)+(10)/(x^6)

\int 3 x + \frac{10}{x ^{6}} d x

2 x^{\frac{3}{2}} - \frac{2}{x ^{5}} + C

Solution steps

\int 3 x + \frac{10}{x ^{6}} 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 3 x d x + \int \frac{10}{x ^{6}} d x

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

\int \frac{10}{x ^{6}} d x = - \frac{2}{x ^{5}}

= 2 x^{\frac{3}{2}} - \frac{2}{x ^{5}}

Add a constant to the solution

= 2 x^{\frac{3}{2}} - \frac{2}{x ^{5}} + C

What is the integral of 3sqrt(x)+(10)/(x^6) ?
The integral of 3sqrt(x)+(10)/(x^6) is 2x^{3/2}-2/(x^5)+C