求助求助不定积分

救救大一小登吧

x^6+1 =(x^2+1)(x^4-x^2+1)
let
x^3= tanu
3x^2 dx = (secu)^2 du
∫ (x^4+1)/(x^6+1) dx
=∫ [(x^4-x^2+1) +x^2]/(x^6+1) dx
=∫ dx/(x^2+1) + ∫x^2/(x^6+1) dx
=arctanx + ∫x^2/(x^6+1) dx
=arctanx + (1/3)∫du
=arctanx + (1/3)u + C
=arctanx + (1/3)arctan(x^3) + C

重庆范本库科技有限公司

2025高等数学教案下载，全新模板doc，海量文档资料，内容清晰完整，涵盖多种行业领域，下载即用，更多精选优质文档模板等您下载!

2025-03-07 02:55广告

立即查看