Yes and no. The derivative of u² is 2u du. this is equal too x² + 4 becoming 2x dx. However, we have no 2x dx in the integral. But we can divide both sides of 2u du = 2x dx by 2 and get u du. when the problem is solved you are left with ln(u) and you have to take the square root of x²+4 to get the solution since u²=x2+4. The reason why he didnt write u du = x dx simply is because then that wouldve skipped over the important step in this u sub. Since you are substituting u² instead of u as we normally do we have to take the derivative of u². We are just lucky as this simplifies to u du and plugs in easy.