What is the integral of x^{-3/4}+4e^x ?

The integral of x^{-3/4}+4e^x is 4x^{1/4}+4e^x+C

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integral of x^{-3/4}+4e^x

\int x^{- \frac{3}{4}} + 4 e^{x} d x

4 x^{\frac{1}{4}} + 4 e^{x} + C

Solution steps

\int x^{- \frac{3}{4}} + 4 e^{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^{- \frac{3}{4}} d x + \int 4 e^{x} d x

\int x^{- \frac{3}{4}} d x = 4 x^{\frac{1}{4}}

\int 4 e^{x} d x = 4 e^{x}

= 4 x^{\frac{1}{4}} + 4 e^{x}

Add a constant to the solution

= 4 x^{\frac{1}{4}} + 4 e^{x} + C

What is the integral of x^{-3/4}+4e^x ?
The integral of x^{-3/4}+4e^x is 4x^{1/4}+4e^x+C