What is the integral of 1/(4y)-1/(\sqrt[4]{y)}+1 ?

The integral of 1/(4y)-1/(\sqrt[4]{y)}+1 is 1/4 ln|y|-4/3 y^{3/4}+y+C

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integral of 1/(4y)-1/(\sqrt[4]{y)}+1

\int \frac{1}{4 y} - \frac{1}{4 y} + 1 d y

\frac{1}{4} ln ∣ y ∣ - \frac{4}{3} y^{\frac{3}{4}} + y + C

Solution steps

\int \frac{1}{4 y} - \frac{1}{4 y} + 1 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{4 y} d y - \int \frac{1}{4 y} d y + \int 1 d y

\int \frac{1}{4 y} d y = \frac{1}{4} ln ∣ y ∣

\int \frac{1}{4 y} d y = \frac{4}{3} y^{\frac{3}{4}}

\int 1 d y = y

= \frac{1}{4} ln ∣ y ∣ - \frac{4}{3} y^{\frac{3}{4}} + y

Add a constant to the solution

= \frac{1}{4} ln ∣ y ∣ - \frac{4}{3} y^{\frac{3}{4}} + y + C

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What is the integral of 1/(4y)-1/(\sqrt[4]{y)}+1 ?
The integral of 1/(4y)-1/(\sqrt[4]{y)}+1 is 1/4 ln|y|-4/3 y^{3/4}+y+C