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

The integral from 1 to e^x of 1/t is x

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integral from 1 to e^x of 1/t

\int_{1}^{e^{x}} \frac{1}{t} d t

x

Solution steps

\int_{1}^{e^{x}} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= [ln ∣ t ∣]_{1}^{e^{x}}

Compute the boundaries:

x

= x

\int_{0}^{\frac{x}{n}} n (1 - x)^{n - 1} d x

\int_{0}^{\frac{π}{2}} x cos (n x) d x

\int_{x^{4}}^{x^{5}} (2 t - 1)^{3} d t

\int_{0}^{s i n (x)} 1 + t^{2} d t

\int_{- 4}^{- 3} x^{2} - (2 x + 15) d x

What is the integral from 1 to e^x of 1/t ?
The integral from 1 to e^x of 1/t is x