Integration help

• sexy girls

  8 May 10, 00:08

  need help integrating this:

  (1 - x tan x^2) dx

  thanks a lot

• wee_ws

  8 May 10, 06:51

  Hi,

    Consider the fact that -x tan x^2 = (-x sin x^2) / (cos x^2), which looks like the form f'(x) / f(x). Thanks.

  Cheers,
  Wen Shih

• sexy girls

  8 May 10, 20:05

  my answer is 1/2 [x + ln |cos x^2|  ] + K

  but its wrong

• wee_ws

  9 May 10, 07:22

  Hi,

    The problem lies with "1/2 x" in your answer. How did it appear if we are integrating 1 with respect to x?

    A good way to check your answer after integration, is to differentiate it to see if you are able to obtain the expression before it was integrated. If we were to differentiate

    1/2 [x + ln |cos x^2|  ] + K,

    we will get 1/2 [1 - (2x sin x^2)/(cos x^2)] = 1/2 - x tan x^2,

    which is not 1 - x tan x^2.

    Thanks.

  Cheers,
  Wen Shih