# Make a substitution to express the integral as a rational function and evaluate the integral. int...

## Question:

Make a substitution to express the integral as a rational function and evaluate the integral.

{eq}\int \frac{dx}{x+2\sqrt{(x-1)}} {/eq}

## Indefinite Integral in Calculus:

The process of finding a function when its derivative is given is called anti-differentiation or integration.

To solve this problem, we'll use the common integral: {eq}\displaystyle \int \frac{1}{u^2+a^2} \ du = \dfrac{1}{a} \ arctan(u/a) {/eq}

We are given:

{eq}\displaystyle \int \frac{dx}{(x+2)\sqrt{x-1}} {/eq}

Apply u-substitution {eq}u=\sqrt{x-1} \rightarrow \ du =...

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