What is the integral of (eln(x))/x ?

The integral of (eln(x))/x is e/2 ln^2(x)+C

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integral of (eln(x))/x

\int \frac{e ln ( x )}{x} d x

\frac{e}{2} ln^{2} (x) + C

Solution steps

\int \frac{e ln ( x )}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e \cdot \int \frac{ln ( x )}{x} d x

Apply u-substitution

: \int u d u

= e \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= e \frac{u ^{2}}{2}

Substitute back

u = ln (x)

= e \frac{ln ^{2} ( x )}{2}

Simplify

e \frac{ln ^{2} ( x )}{2} : \frac{e}{2} ln^{2} (x)

= \frac{e}{2} ln^{2} (x)

Add a constant to the solution

= \frac{e}{2} ln^{2} (x) + C

\int \frac{1}{x ^{2} - 4 x - 3} d x

\int \frac{2 x ^{2}}{( x ^{2} + 5 ) ^{2}} d x

\int \frac{( 2 + ln ( x ) ) ^{3}}{x} d x

cos^{2} (t)

\int \frac{1}{2}

What is the integral of (eln(x))/x ?
The integral of (eln(x))/x is e/2 ln^2(x)+C