1. ## Integration Problems

I've got the following problems and have just learned latex especially in the hope that someone can help me! I'm struggling a bit with this.

1] $\displaystyle \int \displaystyle{\frac{1}{x}} + x^-3 (dx)$

2] $\displaystyle \int \displaystyle{\frac{x^2 + x}{x}} (dx)$

3] $\displaystyle \int 2\sqrt{x} - \displaystyle{\frac{3}{x^3}} (dx)$

4] $\displaystyle \int \sqrt{x} - \displaystyle{\frac{2}{x^2}} (dx)$

5] $\displaystyle \int \displaystyle{\frac{4}{x^3}} - ^7\sqrt{x} (dx)$

Here are the answers to a few I could come up with:

1] $\displaystyle \displaystyle{\frac{1}{x^3}} - \displaystyle{\frac{1}{x}} + c$

2] $\displaystyle \displaystyle{\frac{x^3}{3}} + \displaystyle{\frac{x^2}{2}} + c$

3] $\displaystyle \displaystyle{\frac{4x^3/2}{3}} + \displaystyle{\frac{3}{x}} + c$

This is all I could do can you please help with the rest? It's the first time I've done latex as I say so I'm sorry if it's unreadable.

2. Originally Posted by db5vry
I've got the following problems and have just learned latex especially in the hope that someone can help me! I'm struggling a bit with this.

1] $\displaystyle \int \displaystyle{\frac{1}{x}} + x^-3 (dx)$

2] $\displaystyle \int \displaystyle{\frac{x^2 + x}{x}} (dx)$

3] $\displaystyle \int 2\sqrt{x} - \displaystyle{\frac{3}{x^3}} (dx)$

4] $\displaystyle \int \sqrt{x} - \displaystyle{\frac{2}{x^2}} (dx)$

5] $\displaystyle \int \displaystyle{\frac{4}{x^3}} - ^7\sqrt{x} (dx)$

Here are the answers to a few I could come up with:

1] $\displaystyle \displaystyle{\frac{1}{x^3}} - \displaystyle{\frac{1}{x}} + c$

2] $\displaystyle \displaystyle{\frac{x^3}{3}} + \displaystyle{\frac{x^2}{2}} + c$

3] $\displaystyle \displaystyle{\frac{4x^3/2}{3}} + \displaystyle{\frac{3}{x}} + c$

This is all I could do can you please help with the rest? It's the first time I've done latex as I say so I'm sorry if it's unreadable.
These are the standard integration rules

$\displaystyle \int x^n\, dx = \frac{x^{n+1}}{n+1} + c,\;\;\;n \ne -1$
$\displaystyle \int \frac{1}{x}\, dx = \ln |\,x\,| + c,$
$\displaystyle \int c f\,dx = c\int f\,dx$
$\displaystyle \int f+g\, dx = \int f\,dx + \int g\,dx$

so for example the fifth question

$\displaystyle \int \frac{4}{x^3} - \sqrt[7]{x} \;dx\;=\; 4 \int x^{-3}\, dx - \int x^{\frac{1}{7}} \;dx = 4 \frac{x^{-2}}{-2} - \frac{x^{\frac{8}{7}}}{\frac{8}{7}} + c = -\frac{2}{x^2} - \frac{7}{8} x^{\frac{8}{7}} + c$

You try the rest (expand #2 first).