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

The integral of (3/(x^3)+2x^{5/2}-1) is -3/(2x^2)+4/7 x^{7/2}-x+C

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integral of (3/(x^3)+2x^{5/2}-1)

\int (\frac{3}{x ^{3}} + 2 x^{\frac{5}{2}} - 1) d x

- \frac{3}{2 x ^{2}} + \frac{4}{7} x^{\frac{7}{2}} - x + C

Solution steps

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

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

\int 2 x^{\frac{5}{2}} d x = \frac{4}{7} x^{\frac{7}{2}}

\int 1 d x = x

= - \frac{3}{2 x ^{2}} + \frac{4}{7} x^{\frac{7}{2}} - x

Add a constant to the solution

= - \frac{3}{2 x ^{2}} + \frac{4}{7} x^{\frac{7}{2}} - x + C

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What is the integral of (3/(x^3)+2x^{5/2}-1) ?
The integral of (3/(x^3)+2x^{5/2}-1) is -3/(2x^2)+4/7 x^{7/2}-x+C