IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

liku

Q--

(x

2.cosx)/(1+sinx)

2 .dx (solve & write which property is used)

edison

I =

(x².cosx)/(1+sinx)² .dx

Integration by parts gives

I = x²

cosx/(1+sinx)² .dx -

(2x.cosx)/(1+sinx)² .dx

= x²

cosx/(1+sinx)² .dx - 2x

cosx/(1+sinx)² .dx + 2

cosx/(1+sinx)² .dx

put (1+sinx) = t, then cosx dx = dt

Now you can proceed.

deepak_agarwal

I =

(x².cosx)/(1+sinx)² .dx

Integration by parts gives

I = x²

cosx/(1+sinx)² .dx -

(2x.integral(cosx/(1+sinx)²) .dx)

put (1+sinx) = t, then cosx dx = dt

I=(x^2)((-1)/(1+sinx)) + integral((2x/(1+sinx))dx

Now you can proceed by applyuing by pRTS ON SECOND PART AGAIN