Integral of \( \displaystyle \tan^{2}{\left(x \right)} \)

Problem 4.184 · easy

1. \[ \int \tan^{2}{\left(x \right)}\, dx \]
   integralStart with the integral of the given function.✓ Proved
2. \[ = \int \left(-1 + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx \]
   trig-identityUse the identity tan(x)**2 = sec(x)**2 - 1, where sec(x) = 1/cos(x).✓ Proved
3. \[ = - \int 1\, dx + \int \sec^{2}{\left(x \right)}\, dx \]
   linearitySplit the integral into two parts.✓ Proved
4. \[ = - x + \tan{\left(x \right)} \]
   antiderivativeIntegrate sec(x)**2 and 1 separately.✓ Proved