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Integration help

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1. Really struggling on this, can anyone help??
2. Hello there, the method I use is to simplify (if necessary) the equation, so in the first question 1/x^3 is the same as x^-3.Then you add 1 to the power, then divide your base by the new power, so again in the first question where you have 3x^4----->3x^5----->3/5x^4
Hope this helps.
Anymore questions just shout
3. The integral of ax^n = [a/(n+1)] * x^(n+1). In other words, increase the power of x by 1, and divide the term by this new power.

1/x^2 = x^-2 and sqrt(x) = x^(1/2)

Use these facts and integrate each expression term by term
4. I'll briefly walk through the last one, if you can do that one you can easily do the others.

You raise the power of anything you integrate with respect to, by 1. So as you probably know, if you integrate x with respect to x, you get

So if you integrate

you get

for

This is just equal to
5. I thought I would use an app I have to make a photo of what the above poster (two above now) posted for the rule for integration generally.

Hopefully that's worked
6. (Original post by LewisCroney)
I thought I would use an app I have to make a photo of what the above poster (two above now) posted for the rule for integration generally.

Hopefully that's worked
It hasn't posted properly, so I'm just putting it here for you:

7. (Original post by Zacken)
It hasn't posted properly, so I'm just putting it here for you:

so you need a constant if you aren't integrating between specified limits?
8. (Original post by thefatone)
so you need a constant if you aren't integrating between specified limits?
Yeah you need a constant if doing indefinite integration (without limits). I like to think of it by differentiating a function of x, if it had any constant on the end of it, once it gets differentiated that constant would become 0, no matter what the constant was. So you're just compensating for that there could have been a constant on the end before differentiation. Similarly, if you have the gradient function, the set of curves given by f(x)+c will all have the same gradient, but be translated in the y-direction by c, so it should be intuitive that you would need to compensate for that since you're going from one gradient solution to many possible curves.
9. (Original post by thefatone)
so you need a constant if you aren't integrating between specified limits?
Yes.

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