Your choice of substitution is good. Don't forget dx. That can be overlooked
For instance, #2.
Hello, c_323_h!
Don't be discouraged . . . the first one takes forever
. . and there are a dozen places to make errors (I've made them all).
Let:
. . and
Substitute: .
We have: .
Let:
Substitute: .
Back-substitute
. . Since , we have: .
Back-substitute: Since , then
We have: .
. .
I need a nap . . .
I do these problems in a formal way.Originally Posted by c_323_h
Ignore this, if you do not understand I do not want to confuse you.
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Let,
Then,
--->Denominator.
Express integrand as,
Also, we have,
Thus,
Thus,
Thus,
Thus, you finally have,
Substitute back,
Simplify the inverse trigonometric with trigonometric, to get,
Thus,