[tex] \int_{0}^{t}\frac{\alpha \beta \gamma^\alpha}{(\gamma+\beta t)^\alpha+1}[\math]
comon seriously theres nothing wrong with my latex code....
be back in an hour with the 'wrong' anser they give. got to nip out
i cant
[tex] \int_{0}^{t}\frac{\alpha \beta \gamma^\alpha}{(\gamma+\beta t)^\alpha+1}[\math]
comon seriously theres nothing wrong with my latex code....
be back in an hour with the 'wrong' anser they give. got to nip out
i cant
ah thats it thanks.
yeahits with respect to d $\displaystyle \int_{0}^{t}\frac{\alpha \beta \gamma^\alpha}{(\gamma+\beta t)^{\alpha+1}}dt$ its to the power alpha+1 on the bottom not +1 separately nb
and the answer given is $\displaystyle -\[\frac{\gamma^\alpha}{(\gamma+\beta t)^\alpha}]_{0}^{t}$
im not into the whole change the t to something like s then do ds , i just keep itas dt....but for this particular integral i keep getting $\displaystyle (\alpha+1)$ on the bottom which I cant caancel...something is wrong i just cant figure out if its me or not
my official working goes something like this,,,as i have forgotton the consise way of dealing with the t in the denominator or ,,woould have there been a differential of it on top the use of natural logs..here goes..
$\displaystyle =\int_{0}^{t}\alpha\beta\gamma^\alpha(\gamma+\beta t)^{-(\alpha+1)}dt\\
=\[-\frac{\alpha\beta\gamma^\alpha}{\beta(\alpha+1)(\g amma+\beta t)^\alpha}]_{0}^{t}$ this makes sense right?...obviously this procedes to a wroong answer'!
I don't see any working, just the problem and what you claim to be the correct answer. Presumably you used the power rule for integrating but you appear to have used it incorrectly. The integral of $\displaystyle x^n$ is $\displaystyle \frac{1}{n+1}x^{n+1}$, not $\displaystyle \frac{1}{n}x^{n+ 1}$ as you have used. With $\displaystyle n= -(\alpha+ 1)= -\alpha- 1$, $\displaystyle n+ 1= -\alpha$. The integral of $\displaystyle (\gamma+ \beta t)^{-(\alpha+ 1)}$ is
$\displaystyle -\frac{1}{\alpha\beta}(\gamma+ \beta t)^{-\alpha}$
That will cancel both the $\displaystyle \alpha$ and $\displaystyle \beta$ in the numerator leaving
$\displaystyle -\frac{\gamma^\alpha}{(\gamma+ \beta t)^\alpha}\left]_0^t= 1- \frac{\gamma^\alpha}{(\gamma+ \beta t)^\alpha}$.