Question

(A) : $\int e^x(\log x+x^{-2})dx=e^x(\log x-\frac{1}{x})+c$
(R): $\int e^x\left[f\right(x)+f^{\prime }(x\left)\right]dx=e^{x}f\left(x\right)+c$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not correct explanation of A
• C. A is true but R is false
• D. A is false but R is true.

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

A$=\int e^x(logx+\frac{1}{x^2})dx$

$\int e^x\left[\right(logx-\frac{1}{x})+(\frac{1}{x^2}+\frac{1}{x}\left)\right]dx$

It is in the form of

$\int e^x\left(f\right(x)+f^{\prime }(x\left)\right)dx=e^{x}f\left(x\right)+c$

So the integral is equal to $e^x[logx-\frac{1}{x}]+c$

A: true and

R: true and R explains A.