1. ## integration problems

I'm not sure how to sort out the following:

1. integrationOf (3 + sqrtOf(2x + 5))

2. integrationOf( e^7x-4) dx
limits 1 to 3

limits 1 to 3

3. integrationOf((5-3x)^-1) dx
limits 0 to 1

p.s. what are the tags to use to draw the actual characters? any docs around here?

2. #1:
$\displaystyle \int \left( 3 + \sqrt{2x + 5}\right) dx \: \: = \: \: \int 3 \: dx + \int \sqrt{2x + 5} \: dx$

Imagine $\displaystyle x^{0}$ in front of the 3 for the first integral and use the substitution $\displaystyle u = 2x + 5 \: \: \Rightarrow \: \: du = 2 dx$ for your right.

#2:
$\displaystyle \int_{1}^{3} e^{7x - 4} \: dx$

Use: $\displaystyle u = 7x - 4$. Don't forget to change your limits on your integrand accordingly.

#3:
$\displaystyle \int_{0}^{1} (5-3x)^{-1} \: dx$

Use $\displaystyle u = 5 - 3x \: \: \Rightarrow \: \: du = -3dx$ for your sub. This gives you: $\displaystyle \int_{u(0)}^{u(1)} u^{-1} \frac{du}{-3} = -\frac{1}{3}\int_{5}^{2} u^{-1} \:du$

To generate these images, you use latex. There's a tutorial right here.