Find the integral of $\frac{\sqrt{1+x}-\left(1+x\right)^{-\frac{1}{2}}}{x^2}$

Got another answer? Verify it here!

Learn how to solve integral calculus problems step by step online.

$\int\frac{\sqrt{1+x}-\left(1+x\right)^{-\frac{1}{2}}}{x^2}dx$

Learn how to solve integral calculus problems step by step online. Find the integral of ((1+x)^1/2-(1+x)^(-1/2))/(x^2). Find the integral. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Simplify the expression inside the integral. We can solve the integral \int\frac{1}{\sqrt{1+x}x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sqrt{1+x} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.