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int(sqrt(5-x^(2))dx)/(x^(4))

∫5−x2dxx4 \int \frac{\sqrt{5-x^{2}} d x}{x^{4}}

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Full solution

Q. ∫5−x2dxx4 \int \frac{\sqrt{5-x^{2}} d x}{x^{4}}
  1. Simplify Integral: Let's start by simplifying the integral: ∫5−x2x4dx\int\frac{\sqrt{5-x^{2}}}{x^{4}}dx We can rewrite this as: ∫5−x2x4dx\int\frac{\sqrt{5-x^2}}{x^4} dx
  2. Use Substitution: Now, let's use a substitution to simplify the integral. Let u=x2u = x^2, then du=2xdxdu = 2x dx, or dx=du2xdx = \frac{du}{2x}. Substituting this in, we get: ∫5−uu2⋅du2u\int\frac{\sqrt{5-u}}{u^2} \cdot \frac{du}{2\sqrt{u}}

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