Question

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

• A. 2
• B. 3
• C. 8
• D. 13

Answer 1

Answer: (D)

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