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What is $\int \frac{4t^2}{5t-5}dt$?

I understand I can take out the constant and divide the polynomials to simplify the function. But if I didn't do the division, how then would I integrate this?

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    If you "didn't do the division", then you aren't doing things right, just as if you "don't do the multiplication" you cannot figure out what $3\times(5+2)$ is equal to.2012-01-10

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Another approach (in the end, the same thing): substitute $u=5t-5$.

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    The substitution $t=e^x+1$ also works nicely, but it is basically the same thing...2012-01-10