The correct option is D Third
Consider the polynomial in the denominator x2+3x−4. The radicand is (x+4)(x−1). That is the polynomial has real zeroes.
We know that, "if the polynomial ax2+bx+c has real zeroes α,β 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.