help me

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help me

anonymous · Answer

Evaluate each of the following integrals.

anonymous · Answer

$$\int\limits8te^(7t) dt$$

zepdrix · Answer

$$\huge \int\limits 8t\cdot e^{7t}dt$$The equation tool can take some getting used to :) So this is the problem? The 7 and t are in the exponent right?

anonymous · Answer

yeah

zepdrix · Answer

Hmm so we'll need to apply integration by Parts.

We want t to be our U, because we want it to shrink down to a constant as we progress.
So let's try setting it up like this,$$\large u=8t \;, \qquad dv=e^{7t}dt$$

zepdrix · Answer

So what do you get for your du, and v? :D

anonymous · Answer

du/dt=8

anonymous · Answer

$$e^7t lets apply \ln$$

zepdrix · Answer

woops :) text doesn't work so well in equation tool, heh.

zepdrix · Answer

du/dt = 8 which we can write as,   du = 8 dt

Having trouble integrating that exponential?

anonymous · Answer

yea

zepdrix · Answer

To integrate an exponential like that, you simply get the same thing back, but also you DIVIDE by the coefficient on x.

Think about what happens when you take a DERIVATIVE of e^(7x).
You get 7e^(7x) right?

Well it's the opposite process here.$$\huge dv=e^{7t}dt \qquad \rightarrow \qquad v=\frac{e^{7t}}{7}$$