What is the integral of e^{ln(x)} 1/x ?

The integral of e^{ln(x)} 1/x is x+C

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integral of e^{ln(x)} 1/x

\int e^{l n (x)} \frac{1}{x} d x

x + C

Solution steps

\int e^{l n (x)} \frac{1}{x} d x

e^{l n (x)} \frac{1}{x} = 1

= \int 1 d x

Integral of a constant:

\int a d x = a x

= 1 \cdot x

Simplify

= x

Add a constant to the solution

= x + C

\frac{d y}{d x} = 3 y, y (0) = 2

x \to \frac{5 π}{6} lim (cos (2 x))

\int e^{t} cos (t) d t

\frac{d}{d x} (ln (x x^{2} - 6))

\frac{d}{d x} (sin^{2} (x) + x^{2} sin (x))