# Homework Help: More reduction formulae troubles

1. Aug 15, 2011

### NewtonianAlch

1. The problem statement, all variables and given/known data
$\int$x$^{n}$2$^{x}$dx = $\frac{2}{ln 2}$ - $\frac{n}{ln 2}$ $\int$x$^{n-1}$2$^{x}$dx

For n is greater or equal to 1, find $\int$x$^{3}$2$^{x}$dx

This is a definite integral from 0 to 1

3. The attempt at a solution

My first question is, after reducing this once, you are left with x$^{2}$, and attempting to reduce that again means the constant outside the integral will effectively become 0, therefore the constant term outside the integral will be 0 no matter how many more times you reduce it, and after you do the integral, 0 times the integrated result will be zero. What am I not seeing properly here?

Ignoring that and continuing to do the reduction, I get $\frac{1}{ln 2}$*$\frac{1}{ln 2}$ which doesn't seem right to ignore it anyways.

That is to say, when it becomes x$^{1}$, and you apply the formula again, you'll get $\frac{1}{ln 2}$ outside the integral, then you're left with x$^{0}$ which is 1, and effectively you just integrate 2$^{x}$ which becomes $\frac{1}{ln 2}$2$^{x}$, substituting 0 and 1, and doing the maths, you're left with $\frac{1}{ln 2}$*$\frac{1}{ln 2}$ as the answer.

2. Aug 15, 2011