I'm using a new method learned in class and cannot apply it properly. I made the table of integration and then simplified but still got it wrong. Where did I go wrong?
the method is called tabular integration and it requires that you
take antiderivatives in the $\displaystyle e^{3x}$ column ...
$\displaystyle e^{3x}$
$\displaystyle \frac{1}{3}e^{3x}$
$\displaystyle \frac{1}{9}e^{3x}$
$\displaystyle \frac{1}{27}e^{3x}$
your writing leaves much to be desired ...
$\displaystyle 7x^2 - 4x$ ............... $\displaystyle e^{5x}$
$\displaystyle 14x - 4$ .................. $\displaystyle \frac{1}{5}e^{5x}$
$\displaystyle 14$ ........................ $\displaystyle \frac{1}{25}e^{5x}$
$\displaystyle 0$ ......................... $\displaystyle \frac{1}{125}e^{5x}$
$\displaystyle (7x^2-4x) \cdot \frac{1}{5}e^{5x} - (14x-4) \cdot \frac{1}{25}e^{5x} + 14 \cdot \frac{1}{125}e^{5x} + C$
$\displaystyle e^{5x}\left(\frac{7x^2-4x}{5} - \frac{14x-4}{25} + \frac{14}{125}\right) + C$
your result is the same as mine ... why do you say it's wrong? (you did forget the constant of integration)
I'm going to have to see my teacher about this. I input my answer and it said it was wrong, then input yours and it said it was wrong only to say the correct answer was the one I gave in the first place.
Thanks for your help, time to break some computers!