What is the integral of (12)/(x^2)+2sqrt(x+2) ?

The integral of (12)/(x^2)+2sqrt(x+2) is -(12)/x+4/3 (x+2)^{3/2}+C

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integral of (12)/(x^2)+2sqrt(x+2)

\int \frac{12}{x ^{2}} + 2 x + 2 d x

- \frac{12}{x} + \frac{4}{3} (x + 2)^{\frac{3}{2}} + C

Solution steps

\int \frac{12}{x ^{2}} + 2 x + 2 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{12}{x ^{2}} d x + \int 2 x + 2 d x

\int \frac{12}{x ^{2}} d x = - \frac{12}{x}

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

= - \frac{12}{x} + \frac{4}{3} (x + 2)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{12}{x} + \frac{4}{3} (x + 2)^{\frac{3}{2}} + C

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What is the integral of (12)/(x^2)+2sqrt(x+2) ?
The integral of (12)/(x^2)+2sqrt(x+2) is -(12)/x+4/3 (x+2)^{3/2}+C