What is the integral of e^{ln(x^2)} ?

The integral of e^{ln(x^2)} is (x^3)/3+C

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integral of e^{ln(x^2)}

\int e^{l n (x^{2})} d x

\frac{x ^{3}}{3} + C

Solution steps

\int e^{l n (x^{2})} d x

Apply log rule:

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

= \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{3}}{3} + C

\int sec^{2} (5 x) tan^{6} (5 x) d x

f (x) = x^{2} - 49 x - 456, at x = 2

\frac{d}{d x} (1 + cot^{2} (x))

\int (x^{2} + 8) e^{- x} d x

x \to \infty lim (\frac{6}{x})