Integral Calculus
Definite Integrals
MMTS_Full_Test_22
Grade 12
Question:
The integral $\displaystyle\int_0^1\dfrac{\tan^{-1}x}{1+x}\,dx$ equals
$\pi\log_e 2$
$\dfrac{\pi}{4}\log_e 2$
$\dfrac{\pi}{8}\log_e 2$
$\dfrac{\pi}{2}\log_e 2$
Step-by-Step Solution
Key Concept: Use IBP or the substitution $x=\tan\theta$
By substitution and standard result: $\int_0^1\frac{\tan^{-1}x}{1+x}dx=\frac{\pi}{8}\ln 2$.
Correct Answer: 3