∫2x(x2+2)−4dx=◻
∫2x(x2+2)−4dx=1−3(x2+2)−3+C
Step 1 :Let u=x2+2. Then, du=2xdx.
Step 2 :Rewrite the integral in terms of u: ∫2x(x2+2)−4dx=∫u−4du
Step 3 :Integrate u−4 with respect to u: ∫u−4du=∫u−4+11−4+1du=1−3u−3
Step 4 :Substitute back u=x2+2: 1−3u−3=1−3(x2+2)−3
Step 5 :∫2x(x2+2)−4dx=1−3(x2+2)−3+C