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Integration question

Would anyone be able to tell me what the best way to solve this question intergate x(3x^2-1)^4

i did substitution and got -u^8/8 + u^9/9
Any help would be great thanks


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Avatar for ztibor
ztibor
10
Original post by adl24
Would anyone be able to tell me what the best way to solve this question intergate x(3x^2-1)^4

i did substitution and got -u^8/8 + u^9/9
Any help would be great thanks


Posted from TSR Mobile


Knowing the rules for differentiation (f.e chain rule), and with some intuition you
can see that the derivative of 3x^2-1 is 6x and you need a factor of 6 before x
that xou can to integrate the whole (3x^2-1)^4 function simple as power funtion
So

16⋅∫6x⋅(3x2−1)4dx=(3x2−1)530+C\frac{1}{6}\cdot \int 6x\cdot (3x^2-1)^4 dx=\frac{(3x^2-1)^5}{30}+C

using that

∫f′(x)⋅fn(x)dx=fn+1(x)n+1+C\int f'(x)\cdot f^n(x) dx=\frac{f^{n+1}(x)}{n+1}+C
(edited 10 years ago)
Original post by adl24
Would anyone be able to tell me what the best way to solve this question intergate x(3x^2-1)^4

i did substitution and got -u^8/8 + u^9/9
Any help would be great thanks


Posted from TSR Mobile


Substitute 3x^2 - 1 = t then 6(xdx) = dt

I hope you can take it from here...


Sent from my iPhone
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Avatar for TenOfThem
TenOfThem
18
Original post by adl24
Would anyone be able to tell me what the best way to solve this question intergate x(3x^2-1)^4

i did substitution and got -u^8/8 + u^9/9
Any help would be great thanks


Posted from TSR Mobile


I am intrigued as to your choice of substitution

You can do this by inspection - since the differential of the bracket is just a multiple of the function outside of the bracket

Try differentiating (3x2−1)5(3x^2-1)^5 and see if that helps

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