Question

If \[ \int \frac{x^2-x+1}{x^2+1}\,e^{\cot^{-1}x}\,dx = A(x)e^{\cot^{-1}x}+C, \] then \(A(x)=\)

• A. \(-x\)
• B. \(x\)
• C. \(\sqrt{1-x}\)
• D. \(\sqrt{1+x}\)

Hint:

If the integral is given in the form \[ \int f(x)e^{g(x)}dx=A(x)e^{g(x)}+C, \] differentiate \(A(x)e^{g(x)}\) and compare with the integrand. In MCQs, checking the options is usually the fastest method.

Answer 1

The Correct Option is B