# Math Help - Few Integration Problems

1. ## Few Integration Problems

Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

(excuse me for not yet knowing how to properly type these problems in)

1) Integrate (x-1)/(x^2-4x+5)

2) Integrate ((2x-1)^.5)/(2x+3)

3) Integrate 1/(x+x*x^.5)

2. Originally Posted by emeryj
Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

(excuse me for not yet knowing how to properly type these problems in)

1) Integrate (x-1)/(x^2-4x+5)

2) Integrate ((2x-1)^.5)/(2x+3)

3) Integrate 1/(x+x*x^.5)

(1) $\int \frac{x-1}{x^2-4x+5} \, dx = \int \frac{x-2}{x^2-4x+5} + \frac{1}{(x-2)^2+1} \, dx$

(2) $\int \frac{\sqrt{2x-1}}{(2x-1) + 4} \, dx$

let $u^2 = 2x-1$

(3) $\int \frac{1}{x(1+\sqrt{x})} \, dx$

let $x = u^2$

3. Originally Posted by emeryj
Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

(excuse me for not yet knowing how to properly type these problems in)

1) Integrate (x-1)/(x^2-4x+5)

$\int\frac{x-1}{x^2-4x+5}\,dx$

$=\int\frac{x-2}{x^2-4x+5}\,dx+\int\frac{1}{x^2-4x+5}\,dx$

$=\int\frac{x-2}{x^2-4x+5}\,dx+\int\frac{1}{(x-2)^2+1}\,dx$