What is the integral of x/(e^7x) ?

The integral of x/(e^7x) is 1/(e^7)x+C

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integral of x/(e^7x)

\int \frac{x}{e ^{7} x} d x

\frac{1}{e ^{7}} x + C

Solution steps

\int \frac{x}{e ^{7} x} d x

Cancel the common factor:

x

= \int \frac{1}{e ^{7}} d x

Integral of a constant:

\int a d x = a x

= \frac{1}{e ^{7}} x

Add a constant to the solution

= \frac{1}{e ^{7}} x + C