Step-by-step Solution

Find the integral $\int\frac{1}{x^2\sqrt{4-x^2}}dx$

Go!
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Step-by-step Solution

Problem to solve:

$\int\frac{dx}{x^2\sqrt{4-x^2}}$

Solving method

Learn how to solve integrals of rational functions problems step by step online.

$x=2\sin\left(\theta \right)$

Unlock this full step-by-step solution!

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^2(4-x^2)^0.5))dx. We can solve the integral \int\frac{1}{x^2\sqrt{4-x^2}}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. Factor 4-4\sin\left(\theta \right)^2 by the greatest common divisor 4.

Final Answer

$\frac{-\frac{1}{4}\sqrt{4-x^2}}{x}+C_0$
SnapXam A2
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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

Tips on how to improve your answer:

$\int\frac{dx}{x^2\sqrt{4-x^2}}$

Related Formulas:

1. See formulas

Time to solve it:

~ 0.08 s