Final answer to the problem
$\frac{243}{2}\arcsin\left(\frac{t}{9}\right)-\frac{3}{2}t\sqrt{81-t^2}+C_0$
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Step-by-step Solution
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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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1
Take out the constant $3$ from the integral
$3\int\frac{t^2}{\sqrt{81-t^2}}dt$
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$3\int\frac{t^2}{\sqrt{81-t^2}}dt$
Learn how to solve problems step by step online. Find the integral int((3t^2)/((81-t^2)^(1/2)))dt. Take out the constant 3 from the integral. We can solve the integral 3\int\frac{t^2}{\sqrt{81-t^2}}dt by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dt, we need to find the derivative of t. We need to calculate dt, we can do that by deriving the equation above. Substituting in the original integral, we get.
Final answer to the problem
$\frac{243}{2}\arcsin\left(\frac{t}{9}\right)-\frac{3}{2}t\sqrt{81-t^2}+C_0$
