Integral (Sin[3x+5])/(1+Cos[3x+5]) solved step by step.
First applied substitute method, using the function arguments as substitution
Now,we replace the function argument per u, that is our new argument, and we factorized per 1/3 because du/3=dx
till can’t we directly solve, but we can applied again the substitution method, but now using w as the substitute variable.
And now, we replace w in the function
the latest, we know that integral of 1/x is equal to log(x)
now, replace back from w to cos(u)+1
after, replace back from u to 3x+5
finally, we can say that is integral is
Identities used for solved this exercise.
This method say that the integral will can by for a portion of the original integral by the derivative of this same portion.
If we have
we can say that b=u and du=a’ therefore