∫ex2e2x+3ex+2dx is equal to
12logex+1ex+2+k
12logex−1ex+1+k
logex+1ex+2+k
logex+2ex+1+k
∫ex2e2x+3ex+2dx
Put ex=t
exdx−dt∫exex2+3ex+2dx=∫dtt2+3t+2=∫dtt2+232t+322−322+2
Use ∫1x2−a2dx=12alogx−ax+a+c
=∫dtt+322−122=12⋅12logt+32−12t+32+12+k=log2ex+22ex+4+k=logex+1ex+2+k