求不定积分(x^3)*sqrt(a^2-x^2)
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/12 07:52:39
求不定积分(x^3)*sqrt(a^2-x^2)
设 x= asint => dx = acost dt
则原积分变为:∫(asint)^3√a²-a²sin²t × acost dt
=a^4∫(sint)^3cos²t dt
=a^4∫(sint)^3-(sint)^5 dt
∵ (sint)^3=(-1/4)sin3t+(3/4)sint
(sint)^5=(1/16)sin5t-(5/16)sin3t+(5/8)sint
∴a^4∫(sint)^3-(sint)^5 dt
=a^4∫(-1/16)sin5t+(1/16)sin3t+(1/8)sint dt
=a^4((-1/80)cos5t+(1/48)cos3t+(1/8)cost +C)
则原积分变为:∫(asint)^3√a²-a²sin²t × acost dt
=a^4∫(sint)^3cos²t dt
=a^4∫(sint)^3-(sint)^5 dt
∵ (sint)^3=(-1/4)sin3t+(3/4)sint
(sint)^5=(1/16)sin5t-(5/16)sin3t+(5/8)sint
∴a^4∫(sint)^3-(sint)^5 dt
=a^4∫(-1/16)sin5t+(1/16)sin3t+(1/8)sint dt
=a^4((-1/80)cos5t+(1/48)cos3t+(1/8)cost +C)
sqrt(x^2+1)sinx求不定积分
求不定积分:dy=sqrt(exp(2x)-1) sqrt是开方,exp是e,求高数达人帮忙
求不定积分:dy=sqrt(exp(2x)-1)dx 求高数达人帮忙
·用matlab编写一个文件,实现求函数x*log(1+sqrt(1+x^2))/sqrt(1+x^2)的不定积分和导数
求不定积分sqrt(1+cos x)/sin x
求积分 ∫sqrt(3x*x-2)dx=?
lim (sqrt(x+2)-sqrt(x))/(sqrt(x+1)-sqrt(x)) (X趋近于正无穷)
求x/(x+1)(x+2)(x+3)的不定积分
求不定积分∫dx/(x^2+a^2)^3/2
lim x->0(sqrt(sin(1/x^2)) 求极限
求不定积分x^2/(a^6-x^6)dx
求不定积分∫ x/(x^2+a)dx.