Final answer to the problem
Step-by-step Solution
Specify the solving method
Simplify $\sqrt{e^x}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x$ and $n$ equals $\frac{1}{2}$
Learn how to solve problems step by step online.
$\int\frac{1}{e^{\frac{1}{2}x}}dx$
Learn how to solve problems step by step online. Integrate the function 1/(e^x^1/2) from 0 to infinity. Simplify \sqrt{e^x} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals \frac{1}{2}. Rewrite the fraction \frac{1}{e^{\frac{1}{2}x}} inside the integral as the product of two functions: 1\left(\frac{1}{e^{\frac{1}{2}x}}\right). We can solve the integral \int1\left(\frac{1}{e^{\frac{1}{2}x}}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.