Desarrollar por medio primer teorema fundamental del calculo

$$\begin{align}&\frac{\partial }{\partial x} \int_{a(x)}^{b(x)} f(t)dt = f(b(x))·b'(x)-f(a(x))·a'(x) \end{align}$$

Por tanto, 

$$\begin{align}&\frac{\partial }{\partial x} \int_{3x}^{x^3} (t^3+1)^{10}dt =\\&\\&= (x^9+1)^{10}·3x^2 - (27x^3+1)^{10}·3 \end{align}$$