I need to know how to do the integral from 0 to 1/3 of 4/(1+9x^2).
Also, the indefinite integral of e^(sqrt(2x+4))/(sqrt(2x+4)).
If you can help for either, that would be great!
Also, the indefinite integral of e^(sqrt(2x+4))/(sqrt(2x+4)).
If you can help for either, that would be great!
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1. PI/3
2. e^(sqrt(2x+4)) + CONSTANT
2. e^(sqrt(2x+4)) + CONSTANT
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∫4/(1 + 9x²) dx from 0 to 1/3
4/9*∫dx/(1/9 + x²) from 0 to 1/3
4/9*arctan(3x) eval. from 0 to 1/3
= 4/9*arctan(1) - 0 = 4/9 * (pi/4) = pi/9
4/9*∫dx/(1/9 + x²) from 0 to 1/3
4/9*arctan(3x) eval. from 0 to 1/3
= 4/9*arctan(1) - 0 = 4/9 * (pi/4) = pi/9
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On the second one, try letting u=sqrt(2x+4). What happens to the denominator when you do this?