Find the general indefinite integral

Question

∫ (1 + tan(x)) dx

 

 

ANSWER: tan(x) + C

#17, p404

Answer 1

the integral as stated is integrable --- Integral (1 + tan(x)) dx = Integral dx + Integral (tan(x)dx) = x + Integral([sin(x)/cos(x)]dx = x - Integral[d(cos(x)/cos(x)] = x - ln|cos(x)| + C

Answer 2

Hi,

 

I think you have stated the problem wrong. It should be integral of ( 1+ (tan²(x)) and not (1+tan(x))

 

if it is integral (( 1+ (tan²(x)) , then we can substitute sec² x for 1+ (tan²(x)) since it is an identity.

 

So we have integral (sec² x dx) = tanx+C      (since the derivative of tan(x) is sec² x, then the integral of sec squared                                                                        must be tanx. Also the +C stands for constant as it is an indefinite                                                                              integral)