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

The integral of (2/(x^3)+3/(x^3)+5) is -1/(x^2)-3/(2x^2)+5x+C

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

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

- \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x + C

Solution steps

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

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

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

\int 5 d x = 5 x

= - \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x

Add a constant to the solution

= - \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x + C

What is the integral of (2/(x^3)+3/(x^3)+5) ?
The integral of (2/(x^3)+3/(x^3)+5) is -1/(x^2)-3/(2x^2)+5x+C