What is the integral of e^{ln(x^5)} ?

The integral of e^{ln(x^5)} is (x^6)/6+C

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integral of e^{ln(x^5)}

\int e^{l n (x^{5})} d x

\frac{x ^{6}}{6} + C

Solution steps

\int e^{l n (x^{5})} d x

Apply log rule:

a^{l o g_{a} (b)} = b

= \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= \frac{x ^{6}}{6}

Add a constant to the solution

= \frac{x ^{6}}{6} + C

(2 x - 3)^{4}

\frac{d}{d x} (e^{x} ln (x^{5}))

x^{^{'}} + x = e^{t}

\int_{0}^{15} x 15 - x d x

\int 10 x d x