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

x^{- 3}

\int cot (x) e^{l n (s i n (x))} d x

\int \frac{cos ( 7 t )}{t} d t

\int cos (x) csc^{7} (x) d x

\frac{1}{cos ^{2} ( x )}

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