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Popular >

integral of ln(e^x)

Solution

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

Solution

\frac{x ^{2}}{2} + C

Solution steps

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

Simplify

ln (e^{x}) : x

= \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + C

Graph

Popular Examples

integral of (ln(n))/n

\int \frac{ln ( n )}{n}

(dy)/(dx)=x*y+x/y

\frac{d y}{d x} = x \cdot y + \frac{x}{y}

integral from 1 to 16 of x^{1/2}ln(x)

\int_{1}^{16} x^{\frac{1}{2}} ln (x) d x

derivative of f(x)=x^2+x-6 derivative of

f (x) = x^{2} + x - 6

derivative of 5*sin(x)

\frac{d}{d x} (5 \cdot sin (x))

Frequently Asked Questions (FAQ)

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