∫xcosx+12x3esinx+x2dx

xcosx+12x3esinx+x2dx

  1. A

    logtan-1xesinx+c

  2. B

    log2xesinx+1-12xesinx+1+1+c

  3. C

    log2xesinx+c

  4. D

    none of these

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    I=xcosx+12x3esinx+x2dx

    =xcosx+1x2xesinx+1dx

    Put 2xesinx+1=t

    (2x(esinx)cosx+esinx(2))dx=dt

    2esinx[xcosx+1]dx=dt

    2xesinxxcosx+1xdx=dt

    (t1)xcosx+1xdx=dt

    xcosx+1xdx=dt(t1)

    Now I=1(t1)tdt

    t=z2dt=2zdz

    I=2z(z21)(z)dz

    =212lnz1z+1+c

    where z=t=2xesinx+1

    I=ln2xesinx+112xesinx+1+1+c

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.