How to evaluate the following integral?$\int_1^2\frac{\sqrt{x}}{1+x+x^2+x^3}$

Asked Jul 17 '23 at 07:25

Active Jul 17 '23 at 08:25

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$$\int_1^2\frac{\sqrt{x}}{1+x+x^2+x^3}$$ How to evaluate the following integral? I am trying this question by simplifying the denominator.

The denominator will be $(1+x)(1+x²)$ and then I am thinking for applying partial fraction method to solve the following integral? But can't solve it, because in the numerator it is $\sqrt{x}$. This is my approach.

edited Jul 17 '23 at 08:25

Alv

asked Jul 17 '23 at 07:25

DEB SANKAR ROY

3

Try letting $u = \sqrt{x}$ and do some partial fractions after. – Accelerator Jul 17 '23 at 07:30
But how to evaluate the denominator? Because in the numerator it is sq. Root of x and in the denominator it is x and x². – DEB SANKAR ROY Jul 17 '23 at 07:31
What do you mean by evaluating the denominator? I'm just suggesting that substitution because doing partial fractions from there would be easier. – Accelerator Jul 17 '23 at 07:32
1

Ok. I have understood the way of solution. Thank you very much @ Accelerator. – DEB SANKAR ROY Jul 17 '23 at 07:36

How to evaluate the following integral?$\int_1^2\frac{\sqrt{x}}{1+x+x^2+x^3}$

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