Question

Help with rules of integration

t*(1.1)^t dt

Answer 1

More Parts! :)

Answer 2

\[\large\rm u=t,\qquad\qquad dv=\left(1.1\right)^t~dt\]Do you remember how to find your v? How to integrate this exponential?

Answer 3

ummm its ln 1.1 - ummm ughhh no i don't remember.

Answer 4

General rule for differentiating exponentials:\[\large\rm \frac{d}{dx}a^x\quad=\quad a^x \ln(a)\]

Answer 5

We multiply by the log of the base.
So when we go the other direction, integration,
\[\large\rm \int\limits a^x~dx=\frac{1}{\ln(a)}a^x\]We divide by the log of the base.

Answer 6

so then we have t(1.1)^t - integral (1.1^t)/ln (1.1)

Answer 7

ohhh no thats not it

Answer 8

Let's get our 4 pieces gathered together so there is no confusion,\[\large\rm u=t,\qquad\qquad dv=\left(1.1\right)^t~dt\]\[\large\rm du=dt,\qquad\qquad v=\frac{(1.1)^t}{\ln(1.1)}\]

Answer 9

And I guess you're trying to set up:\[\large\rm uv-\int\limits v~ du\]ya?

Answer 10

ya... so now the integral of v. which is ... gimme a sec

Answer 11

(1.1)^t/ln(1.1)^2

Answer 12

Good good good, you just get another one of those denominators!