Question

Integrate : sec³ x w. r. t. x.

Answer 1

`I = intsec^3x dx`

`I =int secx.sec^2x dx`

`I =secx.intsec^2xdx-int[d/dx(secx).int sec^2x dx] dx`

`I =secx.tanx-int secx.tanx.tanx dx`

`I =secx.tanx-int secx(sec^2x -1)dx`

`I =secx.tanx-int [sec^3x-secx]dx`

`I =secx.tanx-int sec^3x + int secxdx`

`I =secx.tanx - I + log|secx + tanx| + c`

`2I =secx.tanx + log|secx + tanx| + c`

`therefore I =1/2(secx.tanx + log|secx + tanx|) + c`