Question

$\int e^{-x}(1+(1-x)\log x)dx$ is equal to

• A. $(x\log x)e^{x}+C$
• B. $(x^{2}\log x)e^{-x}+C$
• C. $(x^{2}\log x)e^{-2x}+C$
• D. $(x\log x)e^{-x}+C$
• E. $(x\log x)e^{-2x}+C$

Hint:

Logic Tip: In competitive exams, if the integrand looks like a complicated mix of exponentials and algebraic/logarithmic functions, immediately check the options. Differentiating a product rule expression takes seconds, whereas setting up multiple layers of Integration by Parts can take minutes.

Answer 1

The Correct Option is D