What is the integral from 1 to e^8 of 2/x ?

The integral from 1 to e^8 of 2/x is 16

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integral from 1 to e^8 of 2/x

\int_{1}^{e^{8}} \frac{2}{x} d x

16

Solution steps

\int_{1}^{e^{8}} \frac{2}{x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{e^{8}} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{e^{8}}

Compute the boundaries:

8

= 2 \cdot 8

Simplify

= 16

\int_{0}^{1} 2 - x^{2} - x d x

\int_{2}^{5} \frac{1}{( x + 4 )} d x

\int_{1}^{4} x^{4} ln (x) d x

\int_{0}^{9} \frac{185}{( t + 1 ) ^{3}} d t

\int_{1}^{7} \frac{6}{1 - 3 x} d x

What is the integral from 1 to e^8 of 2/x ?
The integral from 1 to e^8 of 2/x is 16