Multiplier for the whole integral

[Muppetmaster]

Homework Statement

$\pi[\int \right[ \frac{\sqrt{x^2+1}}{x^4+sin(x)^2}\left]\;dx$

Homework Equations

As above

The Attempt at a Solution

Is there some sort of identity not sure even where to start this one?

Sorry that pi is obviously meant to be a multiplier for the whole integral if that isn't clear.

It's not actually outside per se.

You can easily put it before the dx in a relevant format relation to the equation.

It's just a constant outside the integral instead of inside so think of it as the +C if that helps.

 

[rock.freak667]

Where did you get this integral from? By observation, it looks like an integral without an elementary anti-derivative.

 

[Muppetmaster]

Where did you get this integral from? By observation, it looks like an integral without an elementary anti-derivative.

In an advanced textbook, I assume there is a solution but it might as you say be some sort of Taylor series type equation?

I admit it's not technically homework but I thought this would be the place to put it?

 

[n1person]

wolfram says "No!" :P

 

[diazona]

Given that you're adding a power of x to a trigonometric function of x in the denominator, I doubt it would be doable. You could of course do a series expansion around some point and integrate each term in the series individually, but I'm not sure if you'd be able to find a closed-form expression for all the series coefficients.

 

[HallsofIvy]

What was the entire statement of the problem? Was it an indefinite integral as you show or a definite integral?