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ò sinx(1 + cos2x) dx
By Tony Ho (P1942) on Tuesday, September 5, 2000 - 12:15 am:

How do you integrate:

ò sinx(1 + cos2x) dx ??

I have been trying to do this for quite a while now, but I must say I am really stuck! I guess you have to make some substitutions using the product formulae or the sum formulae or the trigonometric identities or things like that, but I cannot do it. I appreciate if someone can help.


Tony Ho

By Pras Pathmanathan (Pp233) on Tuesday, September 5, 2000 - 01:37 am:

You don't have to worry about substituting an identity for the cos2x. Instead just try the substitution u=cosx.

So du/dx = -sinx, so -du = sinx dx, and we have that:

ò sinx(1+cos2x)dx
= -ò 1+u2 du
= -u-u3/3 +constant
= -cosx-(cos3x)/3 +constant

This works because you'll notice that we have (-1 times) the derivative of cosx times a function of cosx, so when we do the substitution, the sinx disappears nicely.

Hope that helps,

Pras

By Tony Ho (P1942) on Tuesday, September 5, 2000 - 03:09 pm:

Thanks very much, I am ashamed I haven't noticed something so obvious.