Find the integral $\int\frac{\arcsin\left(x\right)}{x^2}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{\arcsin\left(x\right)}{-x}-\ln\left|\frac{1+\sqrt{1-x^2}}{x}\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

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  • 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
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Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

Learn how to solve integration by trigonometric substitution problems step by step online.

$\int x^{-2}\arcsin\left(x\right)dx$

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Unlock the first 3 steps of this solution

Learn how to solve integration by trigonometric substitution problems step by step online. Find the integral int(arcsin(x)/(x^2))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. We can solve the integral \int x^{-2}\arcsin\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.

Final answer to the problem

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

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Function Plot

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

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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

How to improve your answer:

Main Topic: Integration by Trigonometric Substitution

Trigonometric substitution is the substitution of trigonometric functions for other expressions. One may use the trigonometric identities to simplify certain integrals containing radical expressions.

Used Formulas

See formulas (3)

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