Final answer to the problem
$\frac{6561\cdot 9^{18}x^{19}}{19\sqrt{\left(81\right)^{21}}\sqrt{\left(81-x^2\right)^{19}}}+C_0$
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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
Simplify the expression
Learn how to solve integrals of rational functions problems step by step online.
$729\int\frac{x^{18}}{\sqrt{\left(81-x^2\right)^{21}}}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((9^3x^18)/((81-x^2)^(21/2)))dx. Simplify the expression. We can solve the integral 729\int\frac{x^{18}}{\sqrt{\left(81-x^2\right)^{21}}}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.
Final answer to the problem
$\frac{6561\cdot 9^{18}x^{19}}{19\sqrt{\left(81\right)^{21}}\sqrt{\left(81-x^2\right)^{19}}}+C_0$
