Question

How do I evaluate `inttan (x) sec^3(x) dx`?

Answer 1

I can write the integral as:
`intSin(x)/cos(x)*1/cos^3(x)dx=`
`=intsin(x)/cos^4(x)dx=`
but: `d(cos(x))=-sin(x)dx`
and the integral becomes (multiplying and dividing by `-1`):
`=int(-sin(x))/-cos^4(x)dx=`
`=int1/-cos^4(x)d(cos(x)=`
`=-intcos^(-4)(x)d(cos(x))=`
`=-cos^(-3)(x)/(-3)+c=`
`=cos^(-3)(x)/(3)+c`