What is the integral of 12x^5+1/(x^2)-e^{3x} ?

The integral of 12x^5+1/(x^2)-e^{3x} is 2x^6-1/x-1/3 e^{3x}+C

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integral of 12x^5+1/(x^2)-e^{3x}

\int 12 x^{5} + \frac{1}{x ^{2}} - e^{3 x} d x

2 x^{6} - \frac{1}{x} - \frac{1}{3} e^{3 x} + C

Solution steps

\int 12 x^{5} + \frac{1}{x ^{2}} - 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 12 x^{5} d x + \int \frac{1}{x ^{2}} d x - \int e^{3 x} d x

\int 12 x^{5} d x = 2 x^{6}

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

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

= 2 x^{6} - \frac{1}{x} - \frac{1}{3} e^{3 x}

Add a constant to the solution

= 2 x^{6} - \frac{1}{x} - \frac{1}{3} e^{3 x} + C

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What is the integral of 12x^5+1/(x^2)-e^{3x} ?
The integral of 12x^5+1/(x^2)-e^{3x} is 2x^6-1/x-1/3 e^{3x}+C