Question

Evaluate ${ \rm \int \dfrac{1}{(1 - x)(4 + {x}^{2}) } dx}$​

Answer 1

Answer:

$\int   \rm \dfrac{1}{(1 - x)(4 +  {x}^{2}) }  =  -  \dfrac{1}{5} \:  log| 1 - x| +  \dfrac{1}{10}   \: log| 4 +  {2}^{2} | +  \dfrac{1}{10}  \tan^{ - 1}  \bigg( \dfrac{x}{2}   \bigg )$

Step-by-step explanation:

For detail process please refer the above attachment

Thank you.

86ad3c4b4d236f82ec0947b9709bf740.pdf

Answer 2

$\sf\huge\bold\pink{Answer:}$

$∫ (1−x)(4+ x2)1 \\  = − 51 log∣1−x∣+ 101 log∣4+ 22∣+ 101 tan−1 (2x )$