Why am I wrong?!

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April 18th 2009, 07:29 PM
cammywhite

Why am I wrong?!

$\int \frac 4{(1+2x)^3} dx$

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

$=\frac {4(1+2x)^{-2}} {-2}$

$=-\frac {2}{(1+2x)^2}$

$=- \frac {2}{4x^2+4x+1}$

But the model answer is $=- \frac {1}{4x^2+4x+1}$

Why did I do wrong?!
April 18th 2009, 07:34 PM
mr fantastic

Quote:

Originally Posted by cammywhite

$\int \frac 4{(1+2x)^3} dx$

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

$=\frac {4(1+2x)^{-2}} {-2}$

$=-\frac {2}{(1+2x)^2}$

$=- \frac {2}{4x^2+4x+1}$

But the model answer is $=- \frac {1}{4x^2+4x+1}$

Why did I do wrong?!

$\int \! (ax + b)^n \, dx = \frac{1}{a} \cdot \frac{1}{n+1} (ax + b)^{n+1} + C$ where $n \neq -1$ .

So you forgot the factor of $\frac{1}{a}$ and you (and the book) forgot the '+ C'.

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