Integration By Substitution
Hi Everyone,
I've just been going over this question:
Find the integral of cosh(u)/(1+sinh^2(u))
Now i got the correct answer + tan^-1(sinh(u))
But a step in the process has me confused.
When you substitute x=sinh(u) at the start, the cosh(u)'s cancel and your left with the intergral of 1/(1+x^2) dx could you not just integrate this to get (1/(2x))*(ln(1+x^2)) + C as the derivative of 1/(2x))*(ln(1+x^2)) + C would be 1/(1+x^2) right? or am i just making a silly mistake somewhere?
Cheers
I've just been going over this question:
Find the integral of cosh(u)/(1+sinh^2(u))
Now i got the correct answer + tan^-1(sinh(u))
But a step in the process has me confused.
When you substitute x=sinh(u) at the start, the cosh(u)'s cancel and your left with the intergral of 1/(1+x^2) dx could you not just integrate this to get (1/(2x))*(ln(1+x^2)) + C as the derivative of 1/(2x))*(ln(1+x^2)) + C would be 1/(1+x^2) right? or am i just making a silly mistake somewhere?
Cheers
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