Processing Math: Done

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+1dx=3dx 

which does not cause any problems.

We obtain

503x+1dx=u=3x+1du=3dx=31161udu=31161u12du=31u21+121+1116=3132uu116=921616−11=92164−1=9263=14