Is Integration by parts the only way?

[avocadogirl]

When faced with an integral which contains the product of two functions, must you always default to integration by parts? Is there no alternative method? Perhaps, one intended for more complex functions?

Thank you.

 

[djeitnstine]

No, it is not always the case, sometimes a simple u substitution will work. For instance the integral of the function$$xe^{x^2}$$ w.r.t. x simply let $$u=x^2$$ works fine. However if one cannot identify a proper 'u' then integration by parts will usually be a valid option. There is no 'one' rule when integrating functions or product of functions.