# Intergration (can someone work out)

• Jun 8th 2010, 03:28 AM
cjdyer
Intergration (can someone work out)
i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate

bold letter are powers!

y = 3x6

y = 4x4 +3

y = (5-3x)2

Y = 5 sin 2x

Y = cos 1 x
3

Y = 1 + √x
x

Y = e 3x + 7
e x
• Jun 8th 2010, 03:33 AM
pickslides

$\int x^n~dx = \frac{x^{n+1}}{n+1}+C$

$\int \sin kx~dx = -\frac{1}{k}\cos kx +C$

$\int \cos kx~dx =\frac{1}{k}\sin kx +C$
• Jun 8th 2010, 03:37 AM
cjdyer
Cheers for that but i really need some worked examples so i can contnue with my project
• Jun 8th 2010, 03:42 AM
pickslides

$\int 9x^2~dx = \frac{9x^{2+1}}{2+1}+C= \frac{9x^{3}}{3}+C= 3x^3+C$

what do you get?
• Jun 8th 2010, 03:48 AM
cjdyer
3x7 + c i get to here then dont know what to do?
7
• Jun 8th 2010, 03:50 AM
pickslides
Quote:

Originally Posted by cjdyer
3x7 + c i get to here then dont know what to do?
7

You are finished, this is correct, try the next one.
• Jun 8th 2010, 03:55 AM
cjdyer
4x5 + c?
5
• Jun 8th 2010, 02:09 PM
pickslides
Quote:

Originally Posted by cjdyer

y = 4x4 +3

Here's another example to follow

$\int 5x^3+7~dx = \frac{5x^{3+1}}{3+1}+7x+C=\dots$

The reason for this being

$\int a~dx=ax+C$ for $a,C\in\mathbb{R}$

Quote:

Originally Posted by cjdyer

y = (5-3x)2

And another example for this

Expanding first $(4-2x)^2 = (4-2x)(4-2x) = 16-16x+4x^2$

Now find $\int 16-16x+4x^2~dx$
• Jun 8th 2010, 02:24 PM
Turiski
Quote:

Originally Posted by pickslides

$\int x^n~dx = \frac{x^{n+1}}{n+1}+C$

$\int \sin kx~dx = -\frac{1}{k}\cos kx +C$

$\int \cos kx~dx =\frac{1}{k}\sin kx +C$

Two more rules you'll need:

$\int e^x~dx = e^x$

Assuming u = g(x) $\int f(u)u'~dx = \int f(u)~du$

u in this example then acts like x in the above four.

Example of the last one (I know it's confusing)

$\int 5 \sin 2x ~ dx$

Here $u = 2x$ so $u' = 2$

So $\int \frac{5}{2} \sin (u)u' ~ dx = \int \frac{5}{2} \sin (u) ~ du$

$= \frac{5}{2}(-cos(u)) + C$

$= - \frac{5}{2}cos(2x) + C$
• Jun 8th 2010, 02:40 PM
pickslides
For the last question

$y= \frac{e^{3x}+7}{e^x}= \frac{e^{3x}}{e^x}+ \frac{7}{e^x} = e^{2x}+7e^{-x}
$
• Jun 8th 2010, 02:41 PM
Plato
Quote:

Originally Posted by cjdyer
i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate
bold letter are powers!

Why not learn to post in symbols? You can use LaTeX tags.
$$x^5+9=2$$ gives $x^5+9=2$.