What is the integral of (x^4)/3+5/(x^3) ?

The integral of (x^4)/3+5/(x^3) is (x^5)/(15)-5/(2x^2)+C

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integral of (x^4)/3+5/(x^3)

\int \frac{x ^{4}}{3} + \frac{5}{x ^{3}} d x

\frac{x ^{5}}{15} - \frac{5}{2 x ^{2}} + C

Solution steps

\int \frac{x ^{4}}{3} + \frac{5}{x ^{3}} 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{x ^{4}}{3} d x + \int \frac{5}{x ^{3}} d x

\int \frac{x ^{4}}{3} d x = \frac{x ^{5}}{15}

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

= \frac{x ^{5}}{15} - \frac{5}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{5}}{15} - \frac{5}{2 x ^{2}} + C

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What is the integral of (x^4)/3+5/(x^3) ?
The integral of (x^4)/3+5/(x^3) is (x^5)/(15)-5/(2x^2)+C