© examsiri.com
Question : 136 of 150
Marks:
+1,
-0
Solution:
Let
I=∫x−11(1+x4)−‌‌dx =∫‌‌dx Put
x2=t ⇒2x‌dx=dt ∴I=‌∫ Put
t=tan‌u ⇒dt=sec2udu ∴ I=‌∫ =‌∫du =‌∫du =‌∫cot5u‌cosec‌u‌d‌u =‌∫cot4u‌cosec‌u⋅cot‌u‌d‌u =‌∫(cosec2u−1)2‌cosec‌u‌cot‌u‌d‌u Put
cosec‌u=v ⇒−cosec‌u‌cot‌u‌d‌u=dv ∴I=‌∫(v2−1)2dv =‌∫(v4−2v2+1)dv =[‌−‌+v]+C =[−cosec3u+cosec‌u]+c =[−+]+c =[−+]+c
© examsiri.com
Go to Question: