早教吧作业答案频道 -->数学-->
(2x^4+x)arctanx积分-1到1
题目详情
(2x^4+x)arctanx积分-1到1
▼优质解答
答案和解析
∫[-1,1](2x^4+x)arctanxdx
=∫[-1,1]2x^4arctanxdx+∫[-1,1]xarctanxdx
=2∫[0,1]xarctanxdx
=x^2arctanx|[0,1]-∫[0,1]x^2/(1+x^2)dx
=π/4-x|[0,1]+arctanx|[0,1]
=π/4-1+π/4
=π/2 -1
=∫[-1,1]2x^4arctanxdx+∫[-1,1]xarctanxdx
=2∫[0,1]xarctanxdx
=x^2arctanx|[0,1]-∫[0,1]x^2/(1+x^2)dx
=π/4-x|[0,1]+arctanx|[0,1]
=π/4-1+π/4
=π/2 -1
看了 (2x^4+x)arctan...的网友还看了以下：
已知:a1=4,a(n+1)=an2(即后一项等于前一项的平方)(1)求an(2)比较(1+1/a 2020-05-13 …
数列怎么这么难!1.已知a(1)=3且a(n)=S(n-1)+2^n,求an及Sn.2.已知S(n 2020-06-04 …
已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n 2020-06-27 …
已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n 2020-06-27 …
已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n 2020-06-27 …
已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n 2020-06-27 …
用a^n-b^n=(a-b)(a^(n-1)+a^(n-2)*b+...+ab^(n-2)+b^( 2020-07-14 …
为什么1+a+a^2+a^3+a^4+...+a^(n-1)=(1-a^n)/(1-a)? 2020-07-21 …
已知数列{a下标n}（后都为下标）满足：a1=4an=4-4/a(n-1)此处括号内位下标(n≥2 2020-07-29 …
在数列{an}中,已知a1=1/4,an+1/an=1/4在数列{an}中,已知a1=1/4,a( 2020-08-02 …