Learn how to solve integration by substitution problems step by step online. Find the integral 3int(-1/2(5-4u)^(1/2))du. The integral of a function times a constant (-\frac{1}{2}) is equal to the constant times the integral of the function. Multiply the fraction and term in 3\cdot \left(-\frac{1}{2}\right)\int\sqrt{5-4u}du. We can solve the integral \int\sqrt{5-4u}du by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it v), which when substituted makes the integral easier. We see that 5-4u it's a good candidate for substitution. Let's define a variable v and assign it to the choosen part. Now, in order to rewrite du in terms of dv, we need to find the derivative of v. We need to calculate dv, we can do that by finding the derivative of the equation above.

Find the integral 3int(-1/2(5-4u)^(1/2))du