the integral and derivative of e^x is e^x itself.(adsbygoogle = window.adsbygoogle || []).push({});

I was told that the derivative and integral of e to the ANYTHING power is e to that something power, meaning that:

∫(e^(6x+4x²+5y³))dx is e^(6x+4x²+5y³)

and

d/dx(e^(6x+4x²+5y³)) is e^(6x+4x²+5y³)

However I recently saw an equation in which ∫(e^(ln(2)*x))dx equalled (1/ln(x))*e^(ln(2)*x)

I do not understand what this is…. They said that this had something to do with the reverse chain rule, but this confused me even more…

If the exponent is seen as an "inside part of the function", then

d/dx(x^y)

would = (d/dx)*y*x^(y-1)

instead of just y*x^(y-1)

I'm very confused whether exponents are "inside functions" or not and why ∫(e^(ln(2)*x))dx did not equal e^(ln(2)*x)

Did I learn the wrong information? What am I not understanding? Please help D=

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# Derivative and integral of e^anything

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