Question

Question #a6232

Answer 1

`=\frac{2x^5-10x^3+15x^2-10x-\frac{5}{x^2}}{10}+C`

Explanation:

After simplifying the problem becomes:

`\int(x^4-3x^2+3x+\frac{1}{x^3}-1)dx`

We can apply linearity, which means integrating each term separately, and adding them together at the end.

Remember that a coefficient is multiplied by the term after integration.

`=\intx^4 dx-3\int x^2 dx+3\int x dx+\int\frac{1}{x^3} dx-\int 1 dx`

`=\frac{x^5}{5}-\frac{3x^3}{3}+\frac{3x^2}{2}-\frac{1}{2x^2}-x+C`

You can keep it like this, but here’s a simplified and rewritten answer:

`=\frac{2x^5-10x^3+15x^2-10x-\frac{5}{x^2}}{10}+C`