What is the integral of y^{2y}(ln(y)+1) ?

The integral of y^{2y}(ln(y)+1) is 1/2 y^{2y}+C

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integral of y^{2y}(ln(y)+1)

\int y^{2 y} (ln (y) + 1) d y

\frac{1}{2} y^{2 y} + C

Solution steps

\int y^{2 y} (ln (y) + 1) d y

Apply u-substitution

: \int \frac{1}{2} d u

= \int \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} u

Substitute back

u = y^{2 y}

= \frac{1}{2} y^{2 y}

Add a constant to the solution

= \frac{1}{2} y^{2 y} + C

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What is the integral of y^{2y}(ln(y)+1) ?
The integral of y^{2y}(ln(y)+1) is 1/2 y^{2y}+C