Integrating (x-9)4^x Using Integration by Parts | Homework Help

[MathNoob123]

Homework Statement

I have to evaluate the integral of (x-9)4^xdx

Homework Equations

Integration by parts

The Attempt at a Solution

I setted the (x-9) as D and the 4^x as I. The problem is that I am not sure what the antiderivative of 4^x would be. I am guessing its mostly like 4^x+1 all over x+1. If this is true, then there is another problem. I am not sure of how i could integrate 4^x+1(x+1)^-1. Help is desperate at this moment, since i only have 6 hours to submit my homework. Please give me support. Thanks.

 

[Dick]

4^x is a lot like e^x. In fact, it is e^(ln(4)*x). That's easy to integrate.

 

[MathNoob123]

4^x is a lot like e^x. In fact, it is e^(ln(4)*x). That's easy to integrate.

thank you very much for the assistance.

 

[rootX]

alright Ill try that, thanks for the advice. And by the way do you perhaps know the antiderivative of e^(ln(4)*x)? Because on this one certain problem i had to find the antiderivative of 4^x which i found to be e^(ln(4)*x) but i can't seem to know how to find the antiderivative of e^(ln(4)*x). Is it perhaps e^(ln(4)*x) all over ln(4)x?

thank you for taking your time to help me out. Really appreciate it.

Keep only one thread for one problem.

What's the anti-derivative of e^(x)?
What's the anti-derivative of e^(a.x)?
So, a = ln(4)