How did Muslim traders raise investments given Islam's prohibition of usury?

When the law prohibits interest altogether, it does not prevent it. Many people must borrow, and nobody will lend without such a consideration for the use of their money as is suitable, not only to what can be made by the use of it, but to the difficulty and danger of evading the law. The high rate of interest among all Mahometan nations is accounted for by Mr. Montesqieu, not from their poverty, but partly from this, and partly from the difficulty of recovering the money.

["The Wealth of Nations" - Adam Smith]

It was not so much a question of being able to raise investments, but of being able to do so at an interest rate sustainable for business. Law, be it religious or not, increases artificially the interest rate, thus seriously crippling economic life, but it never effectively eradicates it.

I upvoted Anixx's answer but I would still like to add mine to expand on it in a more middle ages context. Credit for purposes of trade was absolutely legal. In the work Credit as a means of investement in medieval Islamic trade we encounter the following:

The earliest Muslim legal sources now justify the assertion that already in the late eighth century, and possibly earlier, credit arrangements of various types constituted an important feature of both trade and industry.

This was justified on interpretations of the Quran. In the source mentioned above there are several quoted from Muslim scholars describing credit transactions. The first quote comes from Muhammad al-Shaybani's " Book of Partnership ", the earliest Hanafi code, and describes a provision entitling each of the parties to a partnership to buy and sell on credit. Furthermore, unless otherwise stipulated, neither partner requires the express permission of his colleague for the sale on credit of any of their joint property:

This is (the instrument) upon which Fuhlan the son of Fuhlan and Fuhlan the son of Fulan have entered into a partnership. They entered the partnership in a Godfearing manner and with mutual fidelity. They have become partners in all things, acquisitions, and skills, in a total investment partnership. They may sell for cash or credit, and they may buy for cash or credit; and each of them may operate in these matters according to judgment. Their capital is such and such, belonging equally to both of them, and all of it is in their possession. Whatever benefit God, the Exalted, grants them is to be shared equally between them; whatever loss or setback overtakes them is to be borne by them in equal shares. They have entered into a partnership on this basis in the month so and so of the year so and so.

Another important quote, from the same source, is that from Al-Sarakhsi according to whom credit dealings were almost indispensable to successful and profitable trading. To quote:

We hold that selling for credit is part of the practice of merchants, and that it is the most conducive means for the achievement of the investor's goal which is profit. And in most cases, profit can only be achieved by selling for credit and not selling for cash... Proof that selling for credit is an absolute feature of trade is found in His statement, may He be exalted, "unless it be local trade that ye are conducting amongst you." This shows that trade can also be long distant, and this latter type of trade cannot come about except by selling on credit.

Usually islamic banks give loans for a share in the income of the business project as opposed to fixed percent of the loan sum (see mudarabah)

The consumer loans may utilize another scheme: the bank buys, for example, a car and it becomes the bank's property, then you use this car and slowly re-buy it from the bank for greater money. Once you finished, the car becomes yours.