Final answer to the problem
$f\left(x\right)=\frac{1-\sin\left(\pi x\right)+2x^2\arcsin\left(x\right)^2-x^2\arcsin\left(x\right)^2\cos\left(\pi x\right)}{2-\cos\left(\pi x\right)}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- Write in simplest form
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Combine $x^2\arcsin\left(x\right)^2+\frac{1-\sin\left(\pi x\right)}{2-\cos\left(\pi x\right)}$ in a single fraction
$f\left(x\right)=\frac{1-\sin\left(\pi x\right)+x^2\arcsin\left(x\right)^2\left(2-\cos\left(\pi x\right)\right)}{2-\cos\left(\pi x\right)}$
2
Multiply the single term $x^2\arcsin\left(x\right)^2$ by each term of the polynomial $\left(2-\cos\left(\pi x\right)\right)$
$f\left(x\right)=\frac{1-\sin\left(\pi x\right)+2x^2\arcsin\left(x\right)^2-x^2\arcsin\left(x\right)^2\cos\left(\pi x\right)}{2-\cos\left(\pi x\right)}$
Final answer to the problem
$f\left(x\right)=\frac{1-\sin\left(\pi x\right)+2x^2\arcsin\left(x\right)^2-x^2\arcsin\left(x\right)^2\cos\left(\pi x\right)}{2-\cos\left(\pi x\right)}$
