Integral (Sin[3x+5])/(1+Cos[3x+5]) Solved

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.
Substitute method
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

and b=a’
we can say that b=u and du=a’ therefore

Logarithm integral identity

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