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Консультация № 67118
15.12.2006, 14:26
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Уважаемые эксперты, очень прошу, пожалуйста, помогите сделать данное задание! (возникли проблемы при их решении)
Используя прием – непосредственного интегрирования, то есть, используя тождественные преобразования подынтегральных выражений, применяя свойства неопределенного интеграла и
основные формулы интегрирования, найти интегралы:
1. ∫ (10x^2-6^x – 4^2x / 2^x) dx
2. ∫ dx / cos^2 x(1+tg^2 x)
3. ∫(3tg^2 x- ^5√x^2 = 5/x)dx
4. ∫ √3+lnx – 6^√x /x ∙ dx
5. ∫ (2^x+5 - 1/√1-4x2) dx.
Используя прием – непосредственного интегрирования, то есть, используя тождественные преобразования подынтегральных выражений, применяя свойства неопределенного интеграла и
основные формулы интегрирования, найти интегралы:
1. ∫ (10x^2-6^x – 4^2x / 2^x) dx
2. ∫ dx / cos^2 x(1+tg^2 x)
3. ∫(3tg^2 x- ^5√x^2 = 5/x)dx
4. ∫ √3+lnx – 6^√x /x ∙ dx
5. ∫ (2^x+5 - 1/√1-4x2) dx.
Обсуждение
Неизвестный
15.12.2006, 14:51
общий
это ответ
Здравствуйте, XDRIVE!
1.
Т.к.
4^2x / 2^x = 2^(4x)/2^x = 2^(3x)
то
∫ (10x^2-6^x – 2^(3*x) dx =
10*x^3/3- 6^x/ln(6) - 8^x/ln(8)
2)
Т.к.
(1+tg^2 x) = 1/cos^2x
то
∫ dx / cos^2 x(1+tg^2 x) =
=∫ cos^2x / cos^2 x dx=∫1dx =x
3)
tg^2 x представьте ввиде
sin^2x/cos^2x
Далее интегрирование по частям.
В остальном аналогично пп. 1,2.
Удачи!
1.
Т.к.
4^2x / 2^x = 2^(4x)/2^x = 2^(3x)
то
∫ (10x^2-6^x – 2^(3*x) dx =
10*x^3/3- 6^x/ln(6) - 8^x/ln(8)
2)
Т.к.
(1+tg^2 x) = 1/cos^2x
то
∫ dx / cos^2 x(1+tg^2 x) =
=∫ cos^2x / cos^2 x dx=∫1dx =x
3)
tg^2 x представьте ввиде
sin^2x/cos^2x
Далее интегрирование по частям.
В остальном аналогично пп. 1,2.
Удачи!
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