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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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