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

f (x) = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 9

\int 6 sin (2 t) d t

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

f (x) = (x^{3} + 3 x^{2} + 1)^{- 3}

x \to \infty lim (2 - 1)

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