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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

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

Substitute back

u = 4 + e^{x}

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

Add a constant to the solution

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

(x^{''} + x)^{^{'}}

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