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Find the integral $\int x^3\sqrt{\left(1-x^2\right)^{3}}dx$

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Solution

Formulas

Videos

Integral of 1/sqrt(1-x^2)

https://www.youtube.com/watch?v=9AvyXgfNN9E

integral of arcsin x

https://www.youtube.com/watch?v=qwHhwdvTGdY

Algebra 1 - Solve an equation with a rational term 1/x= 3+ 7/x^2+7x ex 2

https://www.youtube.com/watch?v=OjNDpBeMpxI

Tutorial - Solve by factoring when a perfect square y= x^2 - 10x+25

https://www.youtube.com/watch?v=HyuViM0fz4w

Integrals: Trig Substitution 2

https://www.youtube.com/watch?v=fD7MbnXbTls

Tutorial - Solve by factoring when a perfect square 0=x^2+6x+9

https://www.youtube.com/watch?v=F7O02LqPQp0

Function Plot

Plotting: $\frac{-x^{2}\sqrt{\left(1-x^2\right)^{5}}}{7}+\frac{-2\sqrt{\left(1-x^2\right)^{5}}}{35}+C_0$

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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
D□x
∫
∫◻
|◻|
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

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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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