Consider the following function. ∫25−x2​x3​dx (a) Determine an appropriate trigonometric substitution. Use x=5sin(θ), wh

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Consider the following function. ∫25−x2​x3​dx (a) Determine an appropriate trigonometric substitution. Use x=5sin(θ), where −2π​≤θ≤2π​, since the integrand contains the expression 52−x2​. Use x=5tan(θ), where −2π​<θ<2π​, since the integrand contains the expression 52−x2​. Use x=5sec(θ), where 0≤θ<2π​ or π≤θ<23π​, since the integrand contains the expression 52−x2​. (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate integral. ∫25−x2​x3​dx=∫(x)dθ