Question

Avalie a seguinte integral indefinida: ∫(secx tanx+cscxcotx) dx

Answer 1

$\int [{sec(x)tg(x) + csc(x) cot(x)}] dx = \int {sec(x)tg(x) dx + \int csc(x) cot(x)dx$

Mas:

$\dfrac{d}{dx} sec(x) = sec(x)tg(x)\\\\\int d [sec(x)] = \int sec(x)tg(x) dx \\\\\int sec(x)tg(x) dx = sec(x) + C1\\\\\dfrac{d}{dx} csc(x) = - ctg(x)csc(x)\\\int d[csc(x)] = \int ctg(x)csc(x)dx\\\int -ctg(x)csc(x)dx = -csc(x)+C2$

Então:

$\int {sec(x)tg(x) dx + \int csc(x) cot(x)dx = sec(x) - csc(x) + C$