# Math Help - Intergration (can someone work out)

1. ## 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

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

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

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

3. Cheers for that but i really need some worked examples so i can contnue with my project

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

what do you get?

5. 3x7 + c i get to here then dont know what to do?
7

6. 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.

7. 4x5 + c?
5

8. 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 $a,C\in\mathbb{R}$

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 $\int 16-16x+4x^2~dx$

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

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

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

10. For the last question

$y= \frac{e^{3x}+7}{e^x}= \frac{e^{3x}}{e^x}+ \frac{7}{e^x} = e^{2x}+7e^{-x}
$

11. 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 $x^5+9=2$.