1please solve
12 Answers
106Let sin-12x+2(4x2+8x+13)0.5 = x
=> sinx = 2x+2(4x2+8x+13)0.5
=> tanx = 2x+23
1∫ tan-1{(2/3(t)}
so,
tan-1{2/3(t)} =y
(t)2/3=tany
sec2ydy =2/3dt
s0,∫y (3/2) sec2ydy
by parts,
=(3/2)ytany- log(secy)
finally.........
=tan-1{(2/3(x+1)}-log[(4(x2+1)-9)/3]
is this right???????
1completing perfect square of den.
sin- ( 2x+2 / √(2x+2)2+9) nd den substitute 2x+2 = 3tan (theta)
simplified expression which u will get is----
3/2 ∫ (theta)* (sec^2 (theta)) which u can easily solve by parts....
1@biswajit
write 3x as A(8x+8) + B
on solving u will get A=3/8 nd B= -3
den d integral will be converted to 2 simple integral which can be easily solved....