What is the integral of x+x^{11}+x^{-11} ?

The integral of x+x^{11}+x^{-11} is (x^2)/2+(x^{12})/(12)-1/(10x^{10)}+C

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integral of x+x^{11}+x^{-11}

\int x + x^{11} + x^{- 11} d x

\frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}} + C

Solution steps

\int x + x^{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 x d x + \int x^{11} d x + \int x^{- 11} d x

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

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

\int x^{- 11} d x = - \frac{1}{10 x ^{10}}

= \frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}} + C

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\int 64 e^{4 θ} sin (4 θ) d θ

\int x sin (2 x^{\frac{3}{2}}) d x

\int - 2 cos (y) d y

\frac{1}{( 1 - x )}

What is the integral of x+x^{11}+x^{-11} ?
The integral of x+x^{11}+x^{-11} is (x^2)/2+(x^{12})/(12)-1/(10x^{10)}+C