Antiderivative of I am trying to find the antiderivative of but i'mn ot sure how to find this. Can someone maybe give me what formula to use when it involves sin?
Answer & Explanation
Beginner2022-06-26Added 18 answers
Step 1 The beauty of trig is that you can get wildly different looking results depending on how you start. For example take identify: Then you can write . Set then . So now we solve the indefinite integral: Substituting back in for we get
This looks very different but you can see that it's equivalent to the first answer given to your question by remembering the following:
and and finally keeping in mind that C of the two answers is not the same.
Beginner2022-06-27Added 10 answers
Why is this correct? We can take the derivative of our answer to see we get our original function back and that this and our primitive are equal up to a constant.
It is helpful to note these few facts to answer your question about what to do when you have sin or cos in an integrand:
Note that this just involves x, but you can still do your normal u-substitutions as necessary to get it in the form above, as I did.
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