Question

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

Answer 1

Answer:

x(θ) = 5 tan θ

Step-by-step explanation:

Given that:

$\int (25+x^2)^{-6} \ dx$

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