Question

Indefinte integral of sec3xtan3x

Answer 1

`\displaystyle\int\sec3x\tan3x\,\mathrm dx=\frac13\int\mathrm d(\sec 3x)=\frac13\sec3x+C`

or if you meant to use exponents,


`\displaystyle\int\sec^3x\tan^3x\,\mathrm dx=\int\sec x\tan x\sec^2x(\sec^2x-1)\,\mathrm dx=\int(\sec^4x-\sec^2x)\,\mathrm d(\sec x)=\frac15\sec^5x-\frac13\sec^3x+C`