Question

Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.

Short answer

Ans:

$$\begin{gathered} \int \frac{x}{\sqrt{x^2-1}}dxfor41 \\ \int x\sqrt{x^2+1}dxfor42 \\ \int \frac{x^2+9}{x^{\frac{3}{2}}}dxfor46 \end{gathered}$$

Step-by-step solution

Step 1. Given information:

Use trigonometric substitution

Step 2. Finding the three integrals using trigonometric substitution :

The three integrals that can be solved without using a trigonometric substitution are exercises 41,42 and 46.

The integrals are as follows.

41. $\int \frac{x}{\sqrt{x^2-1}}dx$

42. $\int x\sqrt{x^2+1}dx$

46. $\int \frac{x^2+9}{x^{\frac{3}{2}}}dx$