# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_0^{\infty}\left(\frac{1}{\sqrt{e^x}}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{\infty }\frac{1}{e^{\frac{1}{2}x}}dx$

Learn how to solve definite integrals problems step by step online. Integrate 1/(e^x^0.5) from 0 to \infty. Applying the power of a power property. Replace the integral's limit by a finite value. Apply the formula: \frac{a}{x^b}=ax^{-b}, where a=1, b=\frac{1}{2}x and x=e. Solve the integral \int_{0}^{c} e^{-\frac{1}{2}x}dx applying u-substitution. Let u and du be.

$\infty +2$

### Problem Analysis

$\int_0^{\infty}\left(\frac{1}{\sqrt{e^x}}\right)dx$

### Main topic:

Definite integrals

~ 0.08 seconds