1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of definite integral ∫ limits1√3( x 2 x 2+1+ ln ( x (2 x 2 x 2+1))) dx is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of definite integral $\int\limits_1^{\sqrt{3}}\left( x ^{2 x ^2+1}+\ln \left( x ^{\left(2 x ^{2 x ^2+1}\right)}\right)\right) dx$ is equal to

Integrals

Solution:

$I =\int\limits_1^{\sqrt{3}}\left( x ^{ x ^2}\right)^2 \cdot( x +2 x \ln x ) dx ; \operatorname{Put}\left( x ^{ x ^2}\right)= t$
So, $I=\int\limits_1^{3 \sqrt{3}} tdt =\frac{27-1}{2}=\frac{26}{2}=13$.