State the trigonometric substitution you would use to find the indefinite integral. Do not integrate. (25 + x2)−6 dx x(θ) =

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-08-14T06:43:20+02:00

Answer:

x(θ) = 5 tan θ

Step-by-step explanation:

Given that:

[tex]\int (25+x^2)^{-6} \ dx[/tex]

we are to state the trigonometric substitution to be used to find the indefinite integral.

Suppose u is the variable and a is the constant

u = x

a = 5

So; (a² + x²)ⁿ

which is a trigonometric substitution for x = a tanθ

Then,

x(θ) = 5 tan θ

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lhmarianateixeira lhmarianateixeira · Answer 2 · 2022-01-18T11:49:47+01:00

In this exercise we have to use the knowledge of trigonometric substitution to calculate the indefinite integral, so we have that this is:

[tex]x(\theta) = 5 tan \theta[/tex]

Knowing that the indefinite integral corresponds to:

[tex]\int\limits {(25+x^2)^{-6}} \, dx[/tex]

we are to state the trigonometric substitution to be used to find the indefinite integral. Suppose u is the variable and a is the constant:

[tex]u = x\\a = 5\\(a^2 + x^2)^n[/tex]

Which is a trigonometric substitution for:

[tex]x = a tan\theta\\x(\theta) = 5 tan \theta[/tex]

See more about trigonometric substitution at brainly.com/question/21368433