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# Solve the trigonometric integral $\int\arcsin\left(x\right)dx$

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e
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ln
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log
lim
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sin
cos
tan
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sec
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asin
acos
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acot
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$x\arcsin\left(x\right)+\sqrt{1-x^2}+C_0$
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
Can't find a method? Tell us so we can add it.
1

Apply the formula: $\int\arcsin\left(\theta \right)dx$$=\theta \arcsin\left(\theta \right)+\sqrt{1-\theta ^2}+C$

$x\arcsin\left(x\right)+\sqrt{1-x^2}$
2

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$x\arcsin\left(x\right)+\sqrt{1-x^2}+C_0$

##  Final answer to the problem

$x\arcsin\left(x\right)+\sqrt{1-x^2}+C_0$

##  Explore different ways to solve this problem

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

SnapXam A2

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1
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3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.