Evaluate the integral.
-$$\int \frac { d t } { 4 \left( \tan ^ { - 1 } t \right) \left( 1 + t ^ { 2 } \right) }$$
A) $4 \cot ^ { - 1 } \mathrm { t } + \mathrm { C }$
B) $\frac { 1 } { 4 } \ln \left| \tan ^ { - 1 } \mathrm { t } \right| + \mathrm { C }$
C) $\ln \left| 4 \tan ^ { - 1 } t \right| + C$
D) $\frac { 1 } { 4 \left( \tan ^ { - 1 } t \right) ^ { 2 } } + C$

Question

Quizplus · Accepted Answer

Let $u = \tan^{-1} t$. Then $du = \frac{1}{1+t^2} dt$. Substituting, we get$$\int \frac { d t } { 4 \left( \tan ^ { - 1 } t \right) \left( 1 + t ^ { 2 } \right) } = \int \frac { 1 } { 4 u } du = \frac { 1 } { 4 } \ln |u| + C = \frac { 1 } { 4 } \ln |\tan^{-1} t| + C.$$

Evaluate the Integral ∫dt4(tan⁡−1t)(1+t2)\int \frac { d t } { 4 \left( \tan ^ { - 1 } t \right) \left( 1 + t ^ { 2 } \right) }∫4(tan−1t)(1+t2)dt​

Evaluate the Integral $\int \frac { d t } { 4 \left( \tan ^ { - 1 } t \right) \left( 1 + t ^ { 2 } \right) }$