Integration

[EmmaC]

Why does the integration of f(x)= 4x^3+3lnx g(x)= 2(e^x-2) equal x^4 + 3xlnx - 3x + 2e^x-4x + C ?

I can't understand where the 3xlnx - 3x comes from? =S

Regards,
Emma

 

[Aladdin]

Your typing needs a bit of clarification.

You've given two functions ; f(x) = 4x^3+3lnx & g(x) = 2(e^x) - 4 . . .

Actually, the integration of ln(x) dx = xlnx - x " Use integration by parts " ....

Now you can continue ...

 

[soroban]

Hello, EmmaC!

It took a while to "read" your question . . .

\(\displaystyle \text{Why does: }\;\int\left(4x^3+3\ln x + 2e^x-4)\,dx \;\;=\;\;x^4 + 3x\ln x - 3x + 2e^x-4x + C\, ?\)

\(\displaystyle \text{I can't understand where the }3x\ln x - 3x\text{ comes from.}\)

Well, what did YOU get for the second integral?