$\int$ sin^-1[(2x+2)/(4x²+8x+13)^1/2] dx

gokusuper

$\int$ sin^-1[(2x+2)/(4x²+8x+13)^1/2] dx

gokusuper

allamraju

The integral is same as $\int$ Tan^-1(2x+2/3).Now apply by-parts and do.If u want me to post the complete soln,Plz tell me,I will do that.

nunoxic

see consider a triangle :
consider an angle : alpha

Opposite Side = 2x + 2
Adjacent Side = 3
Hypotenuse = root of 4x^2 + 8x + 13 (Pytha)
so same angle can be written as tan -1 (2x + 2 /3)
for convinience put 2x + 2 / 3 = t
solve for tan -1 t using parts and resub

chinmay_saxena01

yup it is same as tan-1(2x+2/3).........just using pythagoras....
and now let 2x+2/3 = t
so dx = 3/2dt
now substitute in question.....
u will get 3/2integration tan -1tdt.....
now by using by parts method......
= 3/2[t tan -1 t -integration 1/1+t^2 * tdt
= 3/2[t tan-1 t - 1/2log(1+t^2)]......simplyfy t/1+t^2 ,,,,by assuming 1+t^2 = u and we get tdt = 1/2du........so the final answer is
3/2(2x+2/3)tan-1(2x+2/3) -3/4log(4x^2+8x+13/9)....

if i helped u plz rate me plzzzz

Ask & Discuss Questions with Community & Experts

sin-1[(2x+2)/(4x2+8x+13)1/2] dx

The integral is same as Tan-1(2x+2/3).Now apply by-parts and do.If u want me to post the complete soln,Plz tell me,I will do that.

$\int$ sin^-1[(2x+2)/(4x²+8x+13)^1/2] dx

The integral is same as $\int$ Tan^-1(2x+2/3).Now apply by-parts and do.If u want me to post the complete soln,Plz tell me,I will do that.