Learn how to solve integral calculus problems step by step online.
$\int\sqrt{\left(x^2+x+1\right)^{3}}dx$
Unlock unlimited step-by-step solutions and much more!
Create a free account and unlock a glimpse of this solution.
Learn how to solve integral calculus problems step by step online. Find the integral int((x^2+x+1)^(3/2))dx. Simplifying. Rewrite the expression \sqrt{\left(x^2+x+1\right)^{3}} inside the integral in factored form. We can solve the integral \int\sqrt{\left(\frac{3}{4}+\left(x+\frac{1}{2}\right)^2\right)^{3}}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.
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
Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.