∫x3−11/3⋅x5dx is equal to

∫x3−11/3x5dx=∫x3−11/3x3⋅x2dx Let x3−1=t⇒x3=t+1Differentiating w.r.t. x, we get3x2=dtdx⇒dx=dt3x2∴ ∫x3-11/3x3⋅x2dx=∫t1/3(t+1)x2dt3x2=13∫t4/3+t1/3dt=13t7/373+t4/343+C=1337t7/3+34t4/3+C=17t7/3+14t4/3+C=17x3−17/3+14x3−14/3+C