?

B

]]>looking for a simplification.

B

just a bit of 'light relief' before I go back to your sequence.

Bob

]]>here's one for you:

]]>Welcome to the forum!

Speaking personally, I don't think there is a guaranteed way of doing integration. With differentiation, once you can do the basic functions (powers, trig, exp, log) and you can do product, quotient and chain rule, you can differentiate anything made up from these.

But there's no such approach for integration.

Sometimes it is 'obvious' that it is a certain function just by looking and remembering the rules for differentiation.

Sometimes it 'looks' like integration by parts may work.

If I see the presence of a function and its derivative then I know substitution will help.

Some other problems also 'yield' to substitution.

Beyond that, it's just trial and improvement for me.

Usually, for exams, the examiners only set ones that can be done by one of the above methods.

There are some fairly simple looking functions that won't give a 'nice' answer at all!

If I got one I could not do, I'd post it here!

Bob

]]>Use the substitution u=8*sin(x)/3

]]>∫(3-3x)/(sqrt(64-9x^2)) dx

]]>