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$\int\frac{x^3}{\sqrt{81-x^2}}dx$

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Solution

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Final answer to the problem

$-\frac{1}{3}x^{2}\sqrt{81-x^2}-54\sqrt{81-x^2}+C_0$
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Step-by-step Solution

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We can solve the integral $\int\frac{x^3}{\sqrt{81-x^2}}dx$ by applying integration method of trigonometric substitution using the substitution

$x=9\sin\left(\theta \right)$

Learn how to solve intégrales de fonctions rationnelles problems step by step online.

$x=9\sin\left(\theta \right)$

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Unlock the first 3 steps of this solution

Learn how to solve intégrales de fonctions rationnelles problems step by step online. int((x^3)/((81-x^2)^(1/2)))dx. We can solve the integral \int\frac{x^3}{\sqrt{81-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 the polynomial 81-81\sin\left(\theta \right)^2 by it's greatest common factor (GCF): 81.

Final answer to the problem

$-\frac{1}{3}x^{2}\sqrt{81-x^2}-54\sqrt{81-x^2}+C_0$

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Plotting: $-\frac{1}{3}x^{2}\sqrt{81-x^2}-54\sqrt{81-x^2}+C_0$

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7
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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
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: Intégrales de fonctions rationnelles

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