# Math Help - integrals with trig

1. ## integrals with trig

Help with this integral:
integral of tcost - sin^2t + cost dt

2. Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.

3. So that's:

$\int tcostdt - \int sin^2tdt - \int costdt$

Try integration by parts for the first integral and a half-angle identity for the second.

Parts:

$\int udv = uv - \int vdu$

4. Originally Posted by s7b
Help with this integral:
integral of tcost - sin^2t + cost dt
The integral can be split into 3 separate integrals: $\int t \cos{t}~dt - \int \sin^2{t}~dt + \int \cos{t}~dt$

The first integral is easily done by parts: $\int t \cos{t}~dt = \int t (\sin{t})' dt = t\sin{t} - \int \sin{t}~dt = t\sin{t} + \cos{t}$

5. Originally Posted by s7b
Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.
Integrate by parts

$u=t \implies du= dt$ and

$dv=\cos(t)dt \implies v=\sin(t)$

don't forget that the formula is

$uv -\int vdu$

6. integrate tcos(t) by parts---do you know the integration by parts formula?

If not use a table of integrals the integral is tsin(t) + cos(t)