Need help on this calculus
2 answers:
The general procedure for solving such integrals is bursting out the odd power of the sin and cos.
I = integral [sin^m(t)+ cos^n(t)] dt
Here since both m and n are odd, I'd say pull out a sin(t)cos(t).
I would leave a cos(t) and convert everything else in terms of sin(t) here. Then substitute u = sin(t) and you are good to go.
You could also do u= cos(t) but then du = -sin(t) dt and I don't like the minus sign.
Hope this helps and stay positive :)
One thing you could do is to expand either a factor of
or
, then expand the integrand. I'll do the first.
You have
which means the integral is equivalent to
Substitute
, so that
. This makes it so that the integral above can be rewritten in terms of
as
Now just use the power rule:
Back-substitute to get the antiderivative back in terms of
:
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