What is the integral of (e^{7ln(x)})/(x^8) ?

The integral of (e^{7ln(x)})/(x^8) is ln|x|+C

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integral of (e^{7ln(x)})/(x^8)

\int \frac{e ^{7 l n (x)}}{x ^{8}} d x

ln ∣ x ∣ + C

Solution steps

\int \frac{e ^{7 l n (x)}}{x ^{8}} d x

Simplify

\frac{e ^{7 l n (x)}}{x ^{8}} : \frac{1}{x}

= \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

\frac{d}{d x} (\frac{x ^{3} - 3}{2 x + 5})

\int \frac{1}{196 + x ^{2}} d x

f (x) = \frac{2}{x + 2}, at x = 1

x \to - 1 lim (2 x^{2} - \frac{3}{x - 1})

\int \frac{b}{a ^{2} x ^{2} - c ^{2}} d x

What is the integral of (e^{7ln(x)})/(x^8) ?
The integral of (e^{7ln(x)})/(x^8) is ln|x|+C