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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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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 integrali di funzioni razionali 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 integrali di funzioni razionali 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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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

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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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0
a
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n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻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: Integrali di funzioni razionali

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