What is the integral of 3/(\sqrt[4]{2x+5)} ?

The integral of 3/(\sqrt[4]{2x+5)} is 2(2x+5)^{3/4}+C

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integral of 3/(\sqrt[4]{2x+5)}

\int \frac{3}{4 2 x + 5} d x

2 (2 x + 5)^{\frac{3}{4}} + C

Solution steps

\int \frac{3}{4 2 x + 5} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{4 2 x + 5} d x

Apply u-substitution

= 3 \cdot \int \frac{1}{2 4 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int \frac{1}{4 u} d u

Apply the Power Rule

= 3 \cdot \frac{1}{2} \cdot \frac{4}{3} u^{\frac{3}{4}}

Substitute back

u = 2 x + 5

= 3 \cdot \frac{1}{2} \cdot \frac{4}{3} (2 x + 5)^{\frac{3}{4}}

Simplify

3 \cdot \frac{1}{2} \cdot \frac{4}{3} (2 x + 5)^{\frac{3}{4}} : 2 (2 x + 5)^{\frac{3}{4}}

= 2 (2 x + 5)^{\frac{3}{4}}

Add a constant to the solution

= 2 (2 x + 5)^{\frac{3}{4}} + C

What is the integral of 3/(\sqrt[4]{2x+5)} ?
The integral of 3/(\sqrt[4]{2x+5)} is 2(2x+5)^{3/4}+C