What is the integral of (162)/(x^3)+2sqrt(x) ?

The integral of (162)/(x^3)+2sqrt(x) is -(81)/(x^2)+4/3 x^{3/2}+C

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integral of (162)/(x^3)+2sqrt(x)

\int \frac{162}{x ^{3}} + 2 x d x

- \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{162}{x ^{3}} + 2 x 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{162}{x ^{3}} d x + \int 2 x d x

\int \frac{162}{x ^{3}} d x = - \frac{81}{x ^{2}}

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

= - \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}} + C

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What is the integral of (162)/(x^3)+2sqrt(x) ?
The integral of (162)/(x^3)+2sqrt(x) is -(81)/(x^2)+4/3 x^{3/2}+C