数学题(有关不定积分运算)- ∫dcost)/(2 - cos^2 t)= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/30 10:34:56
数学题(有关不定积分运算)- ∫dcost)/(2 - cos^2 t)= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)
x){6uӵ^.~Odz9O[7?tݬ?h{uUxԱ:%95RUr@"@ѣYF Z @.PH@KSP_bS4 "}bVK!`5Ffp!!tjei*hAh*!ZI6BBEOlx{)0(EX,.H̳F CaL?E XysH

数学题(有关不定积分运算)- ∫dcost)/(2 - cos^2 t)= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)
数学题(有关不定积分运算)
- ∫dcost)/(2 - cos^2 t)
= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)

数学题(有关不定积分运算)- ∫dcost)/(2 - cos^2 t)= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)
1/(2 - cos^2 t)=1/(√2-cost)(√2+cost)=(1/(2√2) *2√2)/(√2-cost)(√2+cost)
=1/(2√2) *((√2-cost)+(√2+cost))/(√2-cost)(√2+cost)
=1/2√2 * [ 1/(√2-cost)+1/(√2+cost) ]
所以有:
- ∫dcost)/(2 - cos^2 t)
= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)

- ∫dcost)/(2 - cos^2 t)
= - 1/2√2 * ∫[ (√2-cost)+(√2+cost) ]d(cost)/[(√2-cost)(√2+cost)]
= - 1/2√2 * ∫[ 1/(√2-cost)+1/(√2+cost) ]d(cost)