Question

Assertion: $\int x^{x\ln x}dx=x{e}^x+c$

Reason: $x^{x\ln x}=e^x$
The correct answer is:

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

Answer 1

The correct option is D Assertion is false but Reason is true

$\int x^{\frac{x}{\ln x}}dx=x{e}^x+c$

Let $x^{\frac{x}{\ln x}}=f\left(x\right)$

$\ln x^{\frac{x}{\ln x}}=\ln f\left(x\right)$

$=\frac{x}{\ln x}\cdot \ln x=\ln f\left(x\right)$

(1) $f\left(x\right)=e^x$
(2) $\int e^{x}dx=e^{x}dx$

So, Assertion: false
Reason: true