What is the integral of (12x^{11}-(11)/(x^{11)}) ?

The integral of (12x^{11}-(11)/(x^{11)}) is x^{12}+(11)/(10x^{10)}+C

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integral of (12x^{11}-(11)/(x^{11)})

\int (12 x^{11} - \frac{11}{x ^{11}}) d x

x^{12} + \frac{11}{10 x ^{10}} + C

Solution steps

\int 12 x^{11} - \frac{11}{x ^{11}} 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^{11} d x - \int \frac{11}{x ^{11}} d x

\int 12 x^{11} d x = x^{12}

\int \frac{11}{x ^{11}} d x = - \frac{11}{10 x ^{10}}

= x^{12} - (- \frac{11}{10 x ^{10}})

Simplify

= x^{12} + \frac{11}{10 x ^{10}}

Add a constant to the solution

= x^{12} + \frac{11}{10 x ^{10}} + C

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What is the integral of (12x^{11}-(11)/(x^{11)}) ?
The integral of (12x^{11}-(11)/(x^{11)}) is x^{12}+(11)/(10x^{10)}+C