What is the integral of (e^y+4)^5e^y ?

The integral of (e^y+4)^5e^y is ((e^y+4)^6)/6+C

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integral of (e^y+4)^5e^y

\int (e^{y} + 4)^{5} e^{y} d y

\frac{( e ^{y} + 4 ) ^{6}}{6} + C

Solution steps

\int (e^{y} + 4)^{5} e^{y} d y

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = e^{y} + 4

= \frac{( e ^{y} + 4 ) ^{6}}{6}

Add a constant to the solution

= \frac{( e ^{y} + 4 ) ^{6}}{6} + C

What is the integral of (e^y+4)^5e^y ?
The integral of (e^y+4)^5e^y is ((e^y+4)^6)/6+C