# How to integrate $\int\frac{x}{1+x^3}dx$? [duplicate]

How to integrate $\displaystyle \int\frac{x}{1+x^3}dx$? I tried using partial fractions and substitution but it didn't work, thanks.

## marked as duplicate by Xander Henderson, Jean-Claude Arbaut, カカロット, José Carlos Santos calculus StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 17 at 17:41

Partial fractions is indeed the way to go. If you don't want to involve complex numbers, $1 + x^3 = (1+x)(1 - x + x^2)$ so your partial fraction decomposition will look like $$\frac{x}{1+x^3} = \frac{a}{1+x} + \frac{bx+c}{1-x+x^2}$$

For integrating the last term, use completing the square.