What is the integral of y/(x^5+1) ?

The integral of y/(x^5+1) is (y^2)/(2(1+x^5))+C

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integral of y/(x^5+1)

\int \frac{y}{x ^{5} + 1} d y

\frac{y ^{2}}{2 ( 1 + x ^{5} )} + C

Solution steps

\int \frac{y}{x ^{5} + 1} d y

Take the constant out:

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

= \frac{1}{1 + x ^{5}} \cdot \int y d y

Apply the Power Rule

= \frac{1}{1 + x ^{5}} \cdot \frac{y ^{2}}{2}

Simplify

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

= \frac{y ^{2}}{2 ( 1 + x ^{5} )}

Add a constant to the solution

= \frac{y ^{2}}{2 ( 1 + x ^{5} )} + C

What is the integral of y/(x^5+1) ?
The integral of y/(x^5+1) is (y^2)/(2(1+x^5))+C