What is the integral of 2x^3+5/(x^2)-7/x ?

The integral of 2x^3+5/(x^2)-7/x is (x^4)/2-5/x-7ln|x|+C

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integral of 2x^3+5/(x^2)-7/x

\int 2 x^{3} + \frac{5}{x ^{2}} - \frac{7}{x} d x

\frac{x ^{4}}{2} - \frac{5}{x} - 7 ln ∣ x ∣ + C

Solution steps

\int 2 x^{3} + \frac{5}{x ^{2}} - \frac{7}{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 2 x^{3} d x + \int \frac{5}{x ^{2}} d x - \int \frac{7}{x} d x

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

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{x ^{4}}{2} - \frac{5}{x} - 7 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{5}{x} - 7 ln ∣ x ∣ + C

\int (12 x^{\frac{3}{4}} - 9 x^{\frac{5}{3}}) d x

\int \frac{5 x + 1}{x ^{2} - 6 x + 5} d x

\int \frac{3 x ^{2} + 1}{x} d x

\int \frac{3 x - 7 x ^{2}}{x} d x

\int ∣ x ∣ - 1 d x

What is the integral of 2x^3+5/(x^2)-7/x ?
The integral of 2x^3+5/(x^2)-7/x is (x^4)/2-5/x-7ln|x|+C