Let \(I=\int \sqrt{x^2+4x-5}dx\)
=\(\int\sqrt{(x^2+4x+4)-9}dx\)
\(=\int \sqrt{(x+2)^2-(3)^2}dx\)
It is known that,\(\int \sqrt{x^2-a^2}dx=\frac{x}{2}\sqrt{x^2-a^2}-\frac{a^2}{2}\log\mid x+\sqrt{x^2-a^2}\mid+C\)
∴\(I= \frac{(x+2)}{2}\sqrt{x^2+4x-5}-\frac{9}{2}\log\mid (x+2)+\sqrt{x^2+4x-5}\mid +C\)
What is the Planning Process?
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
These are tabulated below along with the meaning of each part.