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Aus Online Mathematik Brückenkurs 2

If we focus on the integrand, then the substitution u=3x+1 seems suitable, since we then get u  which we can integrate. There is also no risk involved in using a linear substitution such as u=3x+1, because the relation between dx and du will be a constant factor,

du=(3x+1)dx=3dx

which does not cause any problems.

We obtain

503x+1dx=udu=3x+1=3dx=31161udu=31161u12du=31 21+1u12+1 116=31 32uu 116=921616−11=92164−1=9263=14.