Question

For the integral $\int \frac{dx}{\sqrt{x^2+3x-4}}$ ,Which Euler's substitution should be used?

• A. First
• B. Third
• C. Second
• D. Cant be solved using Euler's substitu

Answer 1

Answer: (B)

Third

Consider the polynomial in the denominator $x^2+3x-4$. The radicand is $(x+4)(x-1)$. That is the polynomial has real zeroes.
We know that, "if the polynomial $a{x}^2+bx+c$ has real zeroes $\alpha ,\beta$ then we choose third substitution of Euler to simplify the integral.
Since, we have real zeroes for the polynomial in the integrand, the Euler's substitution to be used is $third$.