Rewrite the integral ∫x^3/(√25−x^2) dx using the appropriate trigonometric substitution (do not evaluate the integral).
∫x^3/√(25−x^2) dx
Let x = 5sinθ
then dx = 5cosθ dθ
√(25-x^2) = 5cosθ
and you have
∫x^3/√(25−x^2) dx
∫125sin^3θ/(5cosθ) * 5cosθ dθ = 125∫sin^3θ dθ
The bot botched its attempt using secθ, since 25-x^2 does not work with that.
sec^2θ = 1+tan^2θ
and the rest of its math is just garbage anyway.