Integral SEC(kuadrat) x dx Per Akar 1- tan (kuadrat) x mohon bantuannya yah: )

[tex]\int \frac{sec^2x}{1-tan^2x} dx \\ \\ = \int \frac{1 + tan^2x}{1-tan^2x}dx \\ \\ = \int (\frac{1 + tan^2x}{1-tan^2x}) (\frac{cos^2x}{cos^2x}) dx \\ \\ = \int \frac{cos^2x+sin^2x}{cos^2x-sin^2x}dx \\ \\ = \int \frac{1}{cos(2x)}dx \\ \\ = \int sec(2x) dx [/tex]

[tex]= \int sec(2x) dx \\ \\ misal u = 2x \\ du = 2 dx \\ \\ maka, \\ = \frac{1}{2} \int sec(u) du \\ \\ = \frac{1}{2} \int sec(u) (\frac{sec(u)+tan(u)}{sec(u)+tan(u)}) du \\ \\ = \frac{1}{2} \int \frac{sec^2(u) + sec(u)tan(u)}{sec(u)+tan(u)}du \\ \\ misal, t = sec(u) + tan(u) \\ dt = (sec(u)tan(u) + sec^2u) du \\ \\, [/tex]

[tex]maka, \\ = \frac{1}{2} \int \frac{dt}{t} \\ \\ = \frac{1}{2} ln|t| + C \\ \\ = \frac{1}{2} ln|sec(u)+tan(u)| + C \\ \\ = \frac{1}{2} ln|sec(2x)+tan(2x)| + C [/tex]