Simplify the expression $f\left(x\right)=x^2\arcsin\left(x\right)^2+\frac{1-\sin\left(\pi x\right)}{2-\cos\left(\pi x\right)}$

Step-by-step Solution

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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

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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

$f\left(x\right)=\frac{1-\sin\left(\pi x\right)+2x^2\arcsin\left(x\right)^2-x^2\arcsin\left(x\right)^2\cos\left(\pi x\right)}{2-\cos\left(\pi x\right)}$

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Function Plot

Plotting: $f\left(x\right)-x^2\arcsin\left(x\right)^2+\frac{-1+\sin\left(\pi x\right)}{2-\cos\left(\pi x\right)}$

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a
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g
m
n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Algebraic expressions

An algebraic expression is a group of terms that are separated by $+$ or $-$ signs.

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