42. $\int(2 x-1)^{3} d x$.

The integral of $(2x-1)^3$ with respect to $x$.
Solution. $\int(2 x-1)^{3} d x=\int\left(8 x^{3}-12 x^{2}+6 x-1\right) d x=8 \int x^{3} d x-$ $-12 \int x^{2} d x+6 \int x d x-\int d x=2 x^{4}-4 x^{3}+3 x^{2}-x+C$. By differentiating the result, it is easy to verify that the solution is correct.