Integral, Linear Ordinary differential equation

[ngres1]

I'm doing ordinary differential equation and I need to integrate this

Does anyone know how to do this, I'm told it's more complicated than it looks any help would be really appreciated, thanks.

 

[HallsofIvy]

Are you sure that you weren't told that this is easier than it looks? That is \(\displaystyle \int (1200+ 30t)^{-1/2}(180000- 9.8(1200+ 30t))dt\).

And obvious first step is to let u= 1200+ 30t. Then du= 30dt so dt= (1/30) dt and the integral becomes
\(\displaystyle \int u^{1/2}(180000- 9.8u)(1/30)du= 6000\int u^{1/2} du- \frac{9.8}{30}\int u^{3/2}du\).

 

[ngres1]

Are you sure that you weren't told that this is easier than it looks? That is \(\displaystyle \int (1200+ 30t)^{-1/2}(180000- 9.8(1200+ 30t))dt\).

And obvious first step is to let u= 1200+ 30t. Then du= 30dt so dt= (1/30) dt and the integral becomes
\(\displaystyle \int u^{1/2}(180000- 9.8u)(1/30)du= 6000\int u^{1/2} du- \frac{9.8}{30}\int u^{3/2}du\).

yeah easier I meant i actually ended up figuring it out thanks for your help though!