Annale

How much energy (in kilojoules) is required to convert 130mL of diethyl ether at its boiling point from liquid to vapor if its density is 0.7138 g/mL?

Find the indefinite integral of x^4/1-x^5dx. so far, I have these steps: ∫ f'(x)dx = ∫ x^4/1-x^5dx Let u=1-x^5 du= -5x^4 ∫ u^-1*-1/5du (but I'm not sure if you can technically do -1/5du? this is where I'm getting lost. please help!!)

Find the indefinite integral of (1-sqrtx)/(1+sqrtx)dx I just worked completely through this problem using substitution (u=1+sqrtx) and came to the answer 3+4sqrtx+x+C. This is incorrect. Not sure where I messed up.

Find the indefinite integral. ∫ x^2(1-x)^6 dx I am so lost on this. I let u=1-x so du=-dx. After that, I'm not sure what to do.