(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

i have an equation that i want to solve for b:

[itex]\int _0^1 (a+b x)^2 x^c dx=2[/itex]

2. Relevant equations

\int _0^1 (a+b x)^2 x^c dx=2

given: c>0

3. The attempt at a solution

To evaluate the integral on the left hand side, I expanded the bracket as:

(a+b x)^2=a^2+2abx+(bx)^2.

Then i evaluated the integral and simplifed the result to get:

[itex]\frac{(b^2+2ab+a^2)c^2+(3b^2+8ab+5a^2)c+2b^2+6ab+6a^2}{c^3+6c^2+11c+6}=2[/itex]

and now i'm stuck.

Since we have linear and quadratic powers of b, i don't know how to make b the subject. any ideas will be very much appreciated.

Thank you

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# Solving an equation after integrating

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