To solve the integral , we start by recognizing that it’s in the form of where . To solve, we need to find , which means . The integral then transforms as follows:

Now, integrating gives us . Substituting back for :

So the final result is:

Now, let’s sprinkle in more flavor about integrals!

Understanding how exponential growth works is key, as it appears in various natural phenomena—from population growth to radioactive decay, where integrals help calculate changes over time. Integrating functions like gives us insight into continuous growth, which is foundational in both science and economics!

If you’re ever unsure in your integration journey, remember to check your constants! A common pitfall is forgetting the constant at the end of definite integrals—you’ll miss out on the full picture of possible solutions. Keep practicing and double-checking those derivatives to ensure your integrals are correct!