Question

Integral x4+2/x2+1dx?

Answer 1

`int(x^4+2/x^2+1)dx=1/5x^5-2/x+x+C`

Explanation:

We want to evaluate

`int(x^4+2/x^2+1)dx`

Let's split this up into three separate integrals -- this can be done with sums or differences when integrating.

`int(x^4+2/x^2+1)dx=intx^4dx+int2/x^2dx+intdx`

Now,

`intx^4dx=1/5x^5`

`int2/x^2dx=int2x^-2dx=-2x^-1=-2/x`

`intdx=x`

We'll add in the constant of integration in the end.

Adding these up, we get

`int(x^4+2/x^2+1)dx=1/5x^5-2/x+x+C`

Answer 2

`1/5x^5-2/x+x+C`

where `C` is an arbitrary constant of integration.

Explanation:

`\int (x^4+2/x^2+1)dx`

Hopefully this is what is given in the question.

`\int (x^4+2/x^2+1)dx = \intx^4dx + \int2/x^2dx+\intdx`

`= 1/5x^5-2/x+x+C`

where `C` is an arbitrary constant of integration.