Hint
Now try to use this substitution
By parts, anyone? Do the addition/subtraction (how about 'numerator give-and-take'?!) thing -
Then do integration by parts on the first half...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!