Unlock unlimited step-by-step solutions and much more!
Create a free account and unlock a glimpse of this solution.
Learn how to solve differential calculus problems step by step online. Find the integral int((3x^3-x^22x+-4)/((x^2-3x+2)^1/2))dx. Rewrite the expression \frac{3x^3-x^2+2x-4}{\sqrt{x^2-3x+2}} inside the integral in factored form. We can solve the integral \int\frac{3x^3-x^2+2x-4}{\sqrt{-\frac{1}{4}+\left(x-\frac{3}{2}\right)^2}}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get.
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.