Problem

2x(x2+2)4dx=

Answer

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Answer

2x(x2+2)4dx=13(x2+2)3+C

Steps

Step 1 :Let u=x2+2. Then, du=2xdx.

Step 2 :Rewrite the integral in terms of u: 2x(x2+2)4dx=u4du

Step 3 :Integrate u4 with respect to u: u4du=u4+114+1du=13u3

Step 4 :Substitute back u=x2+2: 13u3=13(x2+2)3

Step 5 :2x(x2+2)4dx=13(x2+2)3+C

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