∫﹙x²+√x³+3﹚/﹙√x﹚dx
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/26 15:24:52
∫﹙x²+√x³+3﹚/﹙√x﹚dx
![∫﹙x²+√x³+3﹚/﹙√x﹚dx](/uploads/image/z/6539447-47-7.jpg?t=%E2%88%AB%EF%B9%99x%26%23178%3B%EF%BC%8B%E2%88%9Ax%26%23179%3B%EF%BC%8B3%EF%B9%9A%EF%BC%8F%EF%B9%99%E2%88%9Ax%EF%B9%9Adx)
d(√x)=1/(2√x) dx => 2d(√x)=1/√x dx
则
∫(x²+√x³+3)/(√x)dx
=2∫﹙x²+√x³+3﹚d(√x)
=2(√x^5/5+x²/4+3√x)+C
=(2/5)√x^5+x²/2+6√x+C
再问: =2(√x^5/5+x²/4+3√x)+C 请问 这一步怎么得出
再答: 2∫﹙x²+√x³+3﹚d(√x) =2∫ [ (√x)^4+(√x)³+3 ] d(√x) =2[ (√x)^5/5 + (√x)^4/4 +3(√x) ]+C =2(√x^5/5+x²/4+3√x)+C
则
∫(x²+√x³+3)/(√x)dx
=2∫﹙x²+√x³+3﹚d(√x)
=2(√x^5/5+x²/4+3√x)+C
=(2/5)√x^5+x²/2+6√x+C
再问: =2(√x^5/5+x²/4+3√x)+C 请问 这一步怎么得出
再答: 2∫﹙x²+√x³+3﹚d(√x) =2∫ [ (√x)^4+(√x)³+3 ] d(√x) =2[ (√x)^5/5 + (√x)^4/4 +3(√x) ]+C =2(√x^5/5+x²/4+3√x)+C