Author Topic: Anti-derivative help please? (Read 1552 times) Tweet Share

username · « **on:** June 26, 2008, 06:31:35 pm »

Hi could someone please help me with anti-deriving these? Thanks!

1. $\int \frac{3z^{4} + 2z}{z^{3}} dz$

2. $\int \frac{(x+1)^{2}}{x} dx$

3. $\int \frac{1}{2x} dx$

4. $\int \frac{3}{(x-1)^{3}} dx$

5. $\int \frac{5}{x} dx$

Mao · « **Reply #1 on:** June 26, 2008, 06:56:34 pm »

for starters, you have forgotten dz and dx for every one of them.

1. $\int \frac{3z^4+2z}{z^3} \; dz = \int 3z + 2z^{-2}\; dz = \frac{3z^2}{2} - \frac{2}{z} + c$

2. $\int \frac{(x+1)^2}{x}\; dx = \int \frac{x^2+2x+1}{x}\; dx = \int x+2+\frac{1}{x}\; dx = \frac{x^2}{2}+2x + ln(x)+c$

3. $\int \frac{1}{2x}\; dx = \frac{1}{2}\int \frac{1}{x}\; dx = \frac{1}{2}ln(x)+c$

4. $\int \frac{3}{(x-1)^3}\; dx = 3\int (x-1)^{-3}\; dx = -\frac{3}{2}(x-1)^{-2}+c$

5. $\int \frac{5}{x}\; dx = 5\int \frac{1}{x}\; dx = 5ln(x)+c$

username · « **Reply #2 on:** June 26, 2008, 06:57:29 pm »

Yess sorry, I'm still new to the latex .. thing.

username · « **Reply #3 on:** June 26, 2008, 06:58:14 pm »

I fixed it! ^_^

username · « **Reply #4 on:** June 26, 2008, 07:01:55 pm »

Mao, for the second one, they had log(x + 1) instead of just log(x). Why is this? >_<

As in

As in: 2. $x^{2}/2 + 2x + log(x+1)$

Mao · « **Reply #5 on:** June 26, 2008, 07:05:38 pm »

Quote from: username on June 26, 2008, 07:01:55 pm

Mao, for the second one, they had log(x + 1) instead of just log(x). Why is this? >_<

As in

As in: 2. $x^{2}/2 + 2x + log(x+1)$

"they" are wrong then....

username · « **Reply #6 on:** June 26, 2008, 07:07:44 pm »

Oh okay, thank you! (Was referring to the Math text book by the way. u_u)

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