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Консультация № 122830
12.02.2008, 16:08
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1
Здраствуйте, меня интересует в ответе на вопрос № 122149
можно ли преобразовать (6+√2)*ln|х-1/√2|/4 + (6-√2)*ln|х+1/√2|/4 +C до 3*ln|2x^2-1|/2+√2*ln|(√2*x-1)/(√2*x+1)|/4?
В такой форме ответ дан в ключа.
можно ли преобразовать (6+√2)*ln|х-1/√2|/4 + (6-√2)*ln|х+1/√2|/4 +C до 3*ln|2x^2-1|/2+√2*ln|(√2*x-1)/(√2*x+1)|/4?
В такой форме ответ дан в ключа.
Обсуждение
Неизвестный
13.02.2008, 03:01
общий
это ответ
Здравствуйте, Lommm!
Конечно, если раскрыть скобки:
3*ln|х-1/√2|/2+√2*ln|х-1/√2|/4 + 3*ln|х+1/√2|/2-√2*ln|х+1/√2|/4
Теперь объединить первое с третьим и второе с четвертым, зная что сумма логарифмов есть логарифм произведения, а разность логарифмов - логарифм частного
3*ln|(х-1/√2)*(х+1/√2)|/2 + √2*ln|(х-1/√2)/(х+1/√2)|/4
Осталось перемножить скобки в первом слагаемом и получим искомое выражение
Конечно, если раскрыть скобки:
3*ln|х-1/√2|/2+√2*ln|х-1/√2|/4 + 3*ln|х+1/√2|/2-√2*ln|х+1/√2|/4
Теперь объединить первое с третьим и второе с четвертым, зная что сумма логарифмов есть логарифм произведения, а разность логарифмов - логарифм частного
3*ln|(х-1/√2)*(х+1/√2)|/2 + √2*ln|(х-1/√2)/(х+1/√2)|/4
Осталось перемножить скобки в первом слагаемом и получим искомое выражение
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