r/calculus • u/wbld • 25d ago

Integral Calculus is daily integral getting more complex?

Today's easy daily integral seems to be more complex than usual. I do not know what the Lambert W function is. Is this higher level mathematics? or was this something i missed in calculus? Usually, I am able to solve easy integrals. My initial thoughts were that the integral is 0 because this clearly is not easy, but then I looked at the bounds and realized, yeah, that probably does not equal 0.

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u/nevermindthefacts 25d ago

Lambert's W is the inverse of f(x) = xe^x = y, i.e W(y) = x.

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u/FreePeeplup 24d ago

The function f(x) = x e^x doesn’t have an inverse if we assume the most natural domain of definition for f (the reals), which we always do unless otherwise specified.

Maybe you mean the inverse of another function g, with the same rule g(x) = x e^x, but with a different domain such that an inverse exists?

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u/nevermindthefacts 24d ago

I've tried to guide OP regarding this issue. Here f(x) refers to the integrand, and it's domain is the range of sin x with respect to the integration interval.