Question

Integrate (1/x + 2/x^3+2)dx

Answer 1

To integrate (1/x + 2/x^3 + 2)dx, we first separate the terms:

∫(1/x + 2/x^3 + 2)dx
= ∫(1/x)dx + ∫(2/x^3)dx + ∫2dx

Now, we integrate each term separately:

∫(1/x)dx = ln|x| + C1, where C1 is the constant of integration

∫(2/x^3)dx = -1/x^2 + C2, where C2 is the constant of integration

∫2dx = 2x + C3, where C3 is the constant of integration

Putting it all together, we get:

ln|x| - 1/x^2 + 2x + C

So, the final solution after integration is ln|x| - 1/x^2 + 2x + C, where C is the constant of integration.