Final answer to the problem
$4\left(\frac{1}{2}\arcsin\left(\frac{x-2}{4}\right)+\frac{\left(x-2\right)\sqrt{-\left(x-2\right)^2+16}}{32}\right)+C_0$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- Load more...
Can't find a method? Tell us so we can add it.
1
Rewrite the expression $\sqrt{12+4x-x^2}$ inside the integral in factored form
$\int\sqrt{-\left(x-2\right)^2+16}dx$
Learn how to solve problems step by step online.
$\int\sqrt{-\left(x-2\right)^2+16}dx$
Learn how to solve problems step by step online. Integrate int((12+4x-x^2)^(1/2))dx. Rewrite the expression \sqrt{12+4x-x^2} inside the integral in factored form. We can solve the integral \int\sqrt{-\left(x-2\right)^2+16}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.
Final answer to the problem
$4\left(\frac{1}{2}\arcsin\left(\frac{x-2}{4}\right)+\frac{\left(x-2\right)\sqrt{-\left(x-2\right)^2+16}}{32}\right)+C_0$
