Homework Sourse1 The substitution u tanx gives sec2xtanxdx xdu 12u2 C
1) The substitution u = tanx gives
?(sec2x*tanx)dx = ?(x)du = 1/2*u2 + C = 1/2* tan2x + C
The substitution u=secx gives
?(sec2x*tanx)dx = ?(x)du = 1/2*u2 + C = 1/2* sec2x + C
Can both integrations be correct? Give reasons for your answer.
?(sec2x*tanx)dx = ?(x)du = 1/2*u2 + C = 1/2* tan2x + C
The substitution u=secx gives
?(sec2x*tanx)dx = ?(x)du = 1/2*u2 + C = 1/2* sec2x + C
Can both integrations be correct? Give reasons for your answer.
Solution
Yes both are correct sec^2x=1+tan^2x so (1/2) sec^2x+c=(1/2)tan^2x+(1/2+c) They both are equal but the integration constants are different.
