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Integrate the function $\frac{x}{16+x^2}$ from 0 to $\infty $

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Solution

Formulas

Videos

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Finding derivative with fundamental theorem of calculus: chain rule | AP®︎ Calculus | Khan Academy

https://www.youtube.com/watch?v=dptES2sb1oc

Calculus - Evaluating a limit by rationalizing the radical, lim(x tends to 0) (sqrt(x + 1) - 1)/x

https://www.youtube.com/watch?v=v8dIvXm03dw

Finding intercepts from an equation | Algebra I | Khan Academy

https://www.youtube.com/watch?v=xGmef7lFc5w

Calculus - How to find the limit of continuous functions, lim(x tends to -3) (x^2 - 8)

https://www.youtube.com/watch?v=RbT5vQajMio

Calculus - Evaluating a limit at infinity horizontal asymptote, lim(x tends to infinity)(2x-1)/(x+1)

https://www.youtube.com/watch?v=miPOf5lXfpw

Function Plot

Plotting: $\frac{x}{16+x^2}$

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Main Topic: Improper Integrals

An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number that is not part of the function's domain, or infinity.

Used Formulas

See formulas (1)

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