What is the integral of (e^{3x}+1/(x^3)-7x^{3/2}) ?

The integral of (e^{3x}+1/(x^3)-7x^{3/2}) is 1/3 e^{3x}-1/(2x^2)-14/5 x^{5/2}+C

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integral of (e^{3x}+1/(x^3)-7x^{3/2})

\int (e^{3 x} + \frac{1}{x ^{3}} - 7 x^{\frac{3}{2}}) d x

\frac{1}{3} e^{3 x} - \frac{1}{2 x ^{2}} - \frac{14}{5} x^{\frac{5}{2}} + C

Solution steps

\int e^{3 x} + \frac{1}{x ^{3}} - 7 x^{\frac{3}{2}} 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 e^{3 x} d x + \int \frac{1}{x ^{3}} d x - \int 7 x^{\frac{3}{2}} d x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

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

\int 7 x^{\frac{3}{2}} d x = \frac{14}{5} x^{\frac{5}{2}}

= \frac{1}{3} e^{3 x} - \frac{1}{2 x ^{2}} - \frac{14}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{3} e^{3 x} - \frac{1}{2 x ^{2}} - \frac{14}{5} x^{\frac{5}{2}} + C

What is the integral of (e^{3x}+1/(x^3)-7x^{3/2}) ?
The integral of (e^{3x}+1/(x^3)-7x^{3/2}) is 1/3 e^{3x}-1/(2x^2)-14/5 x^{5/2}+C