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Wednesday, November 26, 2014
Tuesday, October 14, 2014
មេរៀន រូបមន្ត អាំងតេក្រាល
មេរៀន រូបមន្ត អាំងតេក្រាល
រូបមន្ត និងទំរង់អាំងតេក្រាលមួយចំនួន ទំរង់ស្តង់ដា share សិរីមង្គល
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(អាំងតេក្រាលដោយផ្នែក)
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ទំរង់ជាប់ au+b
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ទំរង់ជាប់ au+b
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ទំរង់ជាប់

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អាំងតេក្រាលជាប់អនុគមន៍ត្រីកោណមាត្រ
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119.![\int \displaystyle \frac{du}{p+qcosau}= \begin{Bmatrix} \displaystyle \frac{2}{a \sqrt{p^{2}-q^{2}}}arctg[ \sqrt{(p-q)/(p+q)}tan \frac{1}{2}au]+c,|p|>|q| \\ \displaystyle \frac{1}{a \sqrt{q^{2}-p^{2}}}ln[ \frac{tan \frac{1}{2}au+ \sqrt{(q+p)/(q-p)}}{tan \frac{1}{2}au- \sqrt{(q+p)/q-p)}}]+c,|p|<|q| \end{Bmatrix} \int \displaystyle \frac{du}{p+qcosau}= \begin{Bmatrix} \displaystyle \frac{2}{a \sqrt{p^{2}-q^{2}}}arctg[ \sqrt{(p-q)/(p+q)}tan \frac{1}{2}au]+c,|p|>|q| \\ \displaystyle \frac{1}{a \sqrt{q^{2}-p^{2}}}ln[ \frac{tan \frac{1}{2}au+ \sqrt{(q+p)/(q-p)}}{tan \frac{1}{2}au- \sqrt{(q+p)/q-p)}}]+c,|p|<|q| \end{Bmatrix}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vefSxJCJNS0hsPJAyKYZ9GkvNQUjLhkH-56kORp4mDXmfoKencQs2HYqk3Mev1ukbmB9eGb5ijR37-CrfLzCbinAx1WBIgsAkF-5ZPfwDPC_ckSkxzwHbPKEMsyFfbeyzluIqPZ9VeiPY3I33MpoJwXGNh4u8UYuRNx0whJ4b4xnsnQP7CpumsT_7prwPwWKy3x-iI_h7yNBw-smWaAaigvdTwRakbvjom0LEEZv4siM537EvAiV3NqZbOSBq37E0TgY_QuDQja6inHVrdBt2jUACAYy_gHaJny7X8EsW3-nJ_rOOcvMwEMw456b8ZtRP59cZwcgCqb0oAPkE0m4Hp-9MQqeD23tJMgnRBqQTX27Ytl_V8R0zA1D9NyW_sacIAayfDatMqm7U3EILnbs4ojjoZFIvvrkId4Ty2ZACSbS8i51VI60uFcdwVItLnx1QsB1FYraemtxJzYYS4qN35pDLVy0qWvUvqaMp05Zb0DVjt4eFGucja1U797Qa9UJ0sOpI7FgoqiCXIiNF9B4ZxuyMudAqYBfElIMHnZgifLGGKOcjjOxUzI6RMcDKRg-l2OY_NDsW-QeqEc5XtaO0cDkMaGLMxGt8nwbHXPIkmsm4Hvcz6rndFiW_QXB6ndw0ztLzQhQNyiDR6O5rWKyPOEo3buuMaJBp8UaUcZ5CuFi-6Oh2hnI5yg6w9tebAQ9gdGkuH6OG3c-LHnh8W9ZXQRDgxkuo5FmyJRublf0vpOqRyFakg8xZko81N9LaZE8VSoE98GE1iZiHjnIaMmGDhDa55XsE=s0-d)
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133.![\int \displaystyle \frac{cosaudu}{sinau \pm cosau}= \pm [ \frac{u}{2}+ \frac{1}{2a}ln|sinau \pm cosau|]+c \int \displaystyle \frac{cosaudu}{sinau \pm cosau}= \pm [ \frac{u}{2}+ \frac{1}{2a}ln|sinau \pm cosau|]+c](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t4eeKp-UShU8Tq0AFYyBl8gtdqU1QRAg4mOJ8SSdvxR_BxS-6TPdhYYfuOaKiVdnctd_iF0A87YohHPDt9icRFatjunFXCLg8GMY9bG_c2r5aALfKYOGM9eqDAztJ4D29M-7rJhdc9jphGB-oACk5v6qygFXKv9gytjEuQltLdhuF6XGZXK0oQJDtMwzqtS53Kvj4fZJ5Qp2W7hYUytQfq8zLWcXJRo05RUiRl3R0qeJ7uswDZLkqoEJlRUfuNTs2wymdJg0N2esIjIRTKsZ76caJibqTs1TS4Ln_UpX6lbCeKyITctjnnmje6Dv1Aai4NvQE5Mq84A537I8E=s0-d)
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អាំងតេក្រាលជាប់អនុគមន៍ច្រាសត្រីកោណមាត្រ
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បើn ជាចំនួនគត់វិជ្ជមាន
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170.![\int ue^{au}sinbudu= \displaystyle \frac{ue^{au}(asinbu-bcosbu)}{a^{2}+b^{2}}- \frac{e^{au}[(a^{2}-b^{2})sinbu-2abcosbu]}{(a^{2}-b^{2})^{2}}+c \int ue^{au}sinbudu= \displaystyle \frac{ue^{au}(asinbu-bcosbu)}{a^{2}+b^{2}}- \frac{e^{au}[(a^{2}-b^{2})sinbu-2abcosbu]}{(a^{2}-b^{2})^{2}}+c](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tpVJQT0oq5lSFR7ks6KrT2vjCI4Bc9so1WujgFyfCV-6Q1cGiXeuYBBO-hLyx7137mdJppDCGvbv3jBSCjHDbOD-i-RV7MpDCPif8i8d06rVlmXvEjcxEd4aCu3vjfuaQkA3f8Ylc3xRtkvJApaPZyapr8XPS1NIzZZuWMo8zMWz2SjSJTQY4Fe_CcDMY8Kmd6__UvcWmopiK_yIGbbdQzX4yOWVYW6v91FPXcc4omLR7J-RfNFzj5Ok2RA8pgFQ_p7zOjmZmMkJs9q35iTyJRkBSIVuN-iEfTw-VbzNuoQhYozcUoYCjLWXaSCYX-d4YgF9-5SpKeVL0VTGpKzlkqbAMuEWJ9Bu4D9LBggutzzBpm9BjJdOKdfnD9U-QfhtHLysw4Zdd8DWZY_JbuOh3mvBqe35lct1PntP_d2Ui5XLKOiRYafIX2Qg=s0-d)
171.![\int ue^{au}cosbudu= \displaystyle \frac{ue^{au}(acosbu+bsinbu)}{a^{2}+b^{2}}- \frac{e^{au}[(a^{2}-b^{2})cosbu+2absinbu]}{(a^{2}-b^{2})^{2}}+c \int ue^{au}cosbudu= \displaystyle \frac{ue^{au}(acosbu+bsinbu)}{a^{2}+b^{2}}- \frac{e^{au}[(a^{2}-b^{2})cosbu+2absinbu]}{(a^{2}-b^{2})^{2}}+c](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vkDQ2YPlM1ftPKp5pSc2o89-Eud6r86Ha6s3QIBQ03ksmyn3VzXAidPEuwPIPiVzyt-YeqZqtqnfXgWVO33ep6DTfUyEIbrrognngHa9LlreWYm9Dst4-YvS_8A74Uu__e3G_MerEaNWsT21Je_onfyX9oTIfVYShuWEogAnQZ0AD_NldgXF1OhOWTMGNUT4JCRLvsEHVLnmpd953EelU4_GQ04V597TA7A_bLp0KjRu7aDHI7zE7J2bGhCRjeZaNsmScDYFMQolJZ9P4GJskgTuNSTsluCA_s0t0iOX42MZn8XnVNofg4rpp9QPhXuQqtzQlWAYaiyrQ2vymK3yhzPs3hrctSsDSF5MbrbmCONJRZQ_o-2osgfLLvfJu7CbkbVXZq_MWi1-3gmHmdXZfmcUWWbDaKn2DrQfFv4qeUbwH9TCvfQ6nZVfFZ1uk=s0-d)
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អាំងតេក្រាលជាប់ lnu
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