Помогите, пожалуйста, найти два интеграла:
1) int 8 * x/e^(x^2) dx
2) int x * e^(x/y)/y^2 dy
1) int 8 * x/e^(x^2) dx = int 4 * 2 * x/e^(x^2) dx = int 4/e^(x^2) d(x^2) =
= | t = x^2 | = int 4/e^t dt = 4 * int e^(-t) dt = 4 * (-1) * e^(-t) + C =
= | t = x^2 | = -4 * e^(-x^2) + C = -4/e^(x^2) + C
2) int x * e^(x/y)/y^2 dy = x * int e^(x/y)/y^2 dy =
= x * int e^(x/y) d(-1/y) = -x * int e^(x/y) d(1/y) = -int e^(x/y) d(x/y) =
= | t = x/y | = -int e^t dt = -e^t + C = | t = x/y | = -e^(x/y) + C
спасибо
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