Решите интегралы S-знак интеграла 1) S xdx / (x^2-20) ^ (1/2) 2) S dx / (x-1) (x-20) 3) S 3xdx / (x-5) (x-15) 4) S (x-9) dx / (x-1) (x-3) 5) S 16dx/x (x^2-16)

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Алгебра

Арий

17 января, 23:13

Решите интегралы S-знак интеграла 1) S xdx / (x^2-20) ^ (1/2) 2) S dx / (x-1) (x-20) 3) S 3xdx / (x-5) (x-15) 4) S (x-9) dx / (x-1) (x-3) 5) S 16dx/x (x^2-16)

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Лизавета · Answer 1

1) = integrate xdx / (sqrt (x^2-20)) [u=x^2-20; du=2xdx]=1/2 integrate du / (sqrt (u)) = 1/2 * (2*sqrt (u)) = sqrt (u) = sqrt (x^2-20) + C

2) = - 1 / (20-1) * ln ((x-20) / (x-1)) = 1/19 * (ln (20-x) - ln (1-x)) + C

3) = 3 integrate xdx / ((x-5) (x-15)) = - 3/2 * (ln (5-x) - 3*ln (15-x)) + C

4) = integrate ((4 / (x-1)) - 3 / (x-3)) dx=4 integrate dx / (x-1) - 3 integrate dx / (x-3) [u=x-1; du=dx] = 4 integrate du/u-3integrate dx / (x-3) = 4*ln (u) - 3 integrate dx / (x-3) = 4*ln (x-1) - 3 integrate dx / (x-3) [u=x-3; du=dx] = 4*ln (x-1) - 3 integrate du/u=4*ln (x-1) - 3*ln (u) = 4*ln (x-1) - 3*ln (x-3) + C