Question

Integrate the function.

∫(13tan²(xse)c²xdx

Answer 1

`\displaystyle13\tan^2x\sec^2x\,\mathrm dx`

Let
`y=\tan x`, so that
`\mathrm dy=\sec^2x\,\mathrm dx`. Then you have


`\displaystyle13\int y^2\,\mathrm dy=\frac{13}3y^3+C`

and so


`\displaystyle\int13\tan^2x\sec^2x\,\mathrm dx=\frac{13}3\tan^3x+C`