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Yeah there is. Get the function to be integrated in to the function whose integration is known. Then integrate it. Leaving it, there's no other shortcut.
therealwinster is pretty much right. Integration is one of the most difficult things to do well. In the end you just have to do a lot of integrals and learn to look for specific things (u-subs, trig, parts, etc). If you can't get it into a good form and you need it for some application you might need to use something like Mathematica or MATLAB to integrate symbolically or numerically (I recommend the former for symbolic stuff).
One step short cut?? Only practicing will determine how many steps it'll take you to get to your answer. I havent heard of a one step short cut. Depends really on what kind of substitution you use, like some posts say undefined integrating consists on changing your original equation look like one of the 24 or so known integrals. Something i found almost as a rule of thumb when solving integrals is if your equation consists of only numbers and x variables its probably u u-sub, if the equation is mixed meaning x variables mixed in with trig then you´ll probably have to integrate it by parts theres is an easy formula to memorize aand if you equation is a fraccion then you should take the road down partial fractions makes it quite easy to integrate if done right, Good Luck