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

The integral of (x^2+2/(x^3)-7) is (x^3)/3-1/(x^2)-7x+C

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

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

\frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x + C

Solution steps

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

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x + C

\int x 3 a + x d x

\int t^{2} - 6 t d t

\int 1 - x x d x

\int 9 x x^{2} + 5 d x

\int \frac{x}{3 x + 6} d x

What is the integral of (x^2+2/(x^3)-7) ?
The integral of (x^2+2/(x^3)-7) is (x^3)/3-1/(x^2)-7x+C