What is the integral of (y^6)/(2y^7+2) ?

The integral of (y^6)/(2y^7+2) is 1/14 ln|2y^7+2|+C

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integral of (y^6)/(2y^7+2)

\int \frac{y ^{6}}{2 y ^{7} + 2} d y

\frac{1}{14} ln 2 y^{7} + 2 + C

Solution steps

\int \frac{y ^{6}}{2 y ^{7} + 2} d y

Apply u-substitution

: \int \frac{1}{14 u} d u

= \int \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} ln ∣ u ∣

Substitute back

u = 2 y^{7} + 2

= \frac{1}{14} ln 2 y^{7} + 2

Add a constant to the solution

= \frac{1}{14} ln 2 y^{7} + 2 + C

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What is the integral of (y^6)/(2y^7+2) ?
The integral of (y^6)/(2y^7+2) is 1/14 ln|2y^7+2|+C