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

The integral of (5x^2+2sqrt(x)+3/(x^2)) is (5x^3)/3+4/3 x^{3/2}-3/x+C

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integral of (5x^2+2sqrt(x)+3/(x^2))

\int (5 x^{2} + 2 x + \frac{3}{x ^{2}}) d x

\frac{5 x ^{3}}{3} + \frac{4}{3} x^{\frac{3}{2}} - \frac{3}{x} + C

Solution steps

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

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

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

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

= \frac{5 x ^{3}}{3} + \frac{4}{3} x^{\frac{3}{2}} - \frac{3}{x}

Add a constant to the solution

= \frac{5 x ^{3}}{3} + \frac{4}{3} x^{\frac{3}{2}} - \frac{3}{x} + C

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What is the integral of (5x^2+2sqrt(x)+3/(x^2)) ?
The integral of (5x^2+2sqrt(x)+3/(x^2)) is (5x^3)/3+4/3 x^{3/2}-3/x+C