## anonymous 4 years ago find the antiderivative of (3x+10)(3x-10)

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1. anonymous

we havent learned rules of multiplication when it comes to antiderivatives yet...so not sure how to handle it

2. Jusaquikie

you have to expand it then you do it like the other ones. $9x^2-100$

3. Jusaquikie

$\frac{ 9x^3 }{ 3 }+100x +C$

4. anonymous

oh ok so the antiderivative is 3x^3-100x

5. anonymous

ya plus the constant

6. anonymous

thx!

7. Jusaquikie

-100 not +100 sorry

8. anonymous

i have another question about antiderivatives if you could help please :)

9. Jusaquikie

sure

10. anonymous

the antiderivative of (x^.5+.5x^-.5)2 (the square root of x plus half times square root of x (in denominator))squared

11. anonymous

because if i do it the other way you did before (add the the expoenent) and divide by it.....it doesnt work because when you take the derivative you gotta take it of the inside function as well

12. Jusaquikie

how bout if you distribute the ^2 ?

13. Jusaquikie

x^2.5+.5x^1.5

14. Jusaquikie

then you can do it like normal

15. anonymous

oooo ok thx

16. anonymous

wouldnt you multiply the 2 not add it .....so it would be x+.5x^-1

17. Jusaquikie

nah think of 10^2 * 10^2 = 100*100=10,000 = 10^4

18. Jusaquikie

or 10^4* 10^2 = 10,000 * 100 = 1,000,000 = 10^6

19. anonymous

but thats because they have the same base.....(a^x)^y = a^xy not a^(x+y)

20. Jusaquikie

x^2 =(x)^2 = (x)x it's all the same

21. Jusaquikie

pull out your calculator and try some examples just plug in any number for x

22. anonymous

23. anonymous

3x^3-100x+constant