What is the integral of x^{sqrt(a)}+1/(x^b)+c^3 ?

The integral of x^{sqrt(a)}+1/(x^b)+c^3 is (x^{sqrt(a)+1}(sqrt(a)-1))/(a-1)+(x^{-b+1})/(-b+1)+c^3x+C

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integral of x^{sqrt(a)}+1/(x^b)+c^3

\int x^{a} + \frac{1}{x ^{b}} + c^{3} d x

\frac{x ^{a + 1} ( a - 1 )}{a - 1} + \frac{x ^{- b + 1}}{- b + 1} + c^{3} x + C

Solution steps

\int x^{a} + \frac{1}{x ^{b}} + c^{3} 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^{a} d x + \int \frac{1}{x ^{b}} d x + \int c^{3} d x

\int x^{a} d x = \frac{x ^{a + 1} ( a - 1 )}{a - 1}

\int \frac{1}{x ^{b}} d x = \frac{x ^{- b + 1}}{- b + 1}

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

= \frac{x ^{a + 1} ( a - 1 )}{a - 1} + \frac{x ^{- b + 1}}{- b + 1} + c^{3} x

Add a constant to the solution

= \frac{x ^{a + 1} ( a - 1 )}{a - 1} + \frac{x ^{- b + 1}}{- b + 1} + c^{3} x + C

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