∫ t sin t^2 dt?

Question

identify u
integration formula.

Answer 1

u = t^2
du = 2t dt
dt = du / (2t)

int(t sin(t^2) dt)
=int((1/2) sin(u) du)
= -(1/2)cos(u) + C
= -(cos(t^2)) / 2 + C

Answer 2

∫ t sin t^2 dt
u = t^2
du = 2tdt

∫ t sin t^2 dt
= (1/2)∫ sin u du
= (1/2)*(-cos u) + c
= -(cos u)/2 + c
= -(cos t^2)/2 + c

Answer 3

let u = t²
du = 2t dt
du / 2 = t dt
I = (1/2) ∫ sin u du
I = (- 1/2) cos u + C
I = (- 1/2) cos t² + C

Answer 4

http://en.wikipedia.org/wiki/Integration_by_parts

Now do your own homework, lazy face!

(Or make this program
http://labs.imranyusuff.net/tabular_integration/
do it for you)