What is the integral of 1/4 x^{-3/4} ?

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

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integral of 1/4 x^{-3/4}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: 4 x^{\frac{1}{4}}

= \frac{1}{4} \cdot 4 x^{\frac{1}{4}}

Simplify

\frac{1}{4} \cdot 4 x^{\frac{1}{4}} : x^{\frac{1}{4}}

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

Add a constant to the solution

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

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