求高数大神解不定积分 共3题,要过程!感谢!
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求高数大神解不定积分 共3题,要过程!感谢!
![求高数大神解不定积分 共3题,要过程!感谢!](/uploads/image/z/6025980-12-0.jpg?t=%E6%B1%82%E9%AB%98%E6%95%B0%E5%A4%A7%E7%A5%9E%E8%A7%A3%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86+%E5%85%B13%E9%A2%98%2C%E8%A6%81%E8%BF%87%E7%A8%8B%21%E6%84%9F%E8%B0%A2%21)
积分(0,1):x^2/(1+x^2)^2
=积分(1/((1+x^2))-1/(1+x^2)^2)
=argtanx-1/2*(arctanx+x/(1+x^2))|(0,1)
=1/2*[argtanx -x/(1+x^2)]|(0,1)
=1/2(π/4-1/2)=π/8-1/4
f^n (x)=(-1)^(n+1) *xe^-x+1/2*e^(-x)*[1+(-1)^n]
f^n(0)=1/2*[1+(-1)^n]
积分(0,1):xf''(2x)dx
=积分(0,1):1/4* 2xf''(2x)d2x
=积分(0,2):1/4* tf''(t)dt
=1/4(xf'-积分f'dt)|(0,2)
=1/4(xf'(t)-f(t))|(0,2)
=1/4(2f'(2)-0f(0)-f(2)+f(0))=1/4(4-4+1)=1/4
=积分(1/((1+x^2))-1/(1+x^2)^2)
=argtanx-1/2*(arctanx+x/(1+x^2))|(0,1)
=1/2*[argtanx -x/(1+x^2)]|(0,1)
=1/2(π/4-1/2)=π/8-1/4
f^n (x)=(-1)^(n+1) *xe^-x+1/2*e^(-x)*[1+(-1)^n]
f^n(0)=1/2*[1+(-1)^n]
积分(0,1):xf''(2x)dx
=积分(0,1):1/4* 2xf''(2x)d2x
=积分(0,2):1/4* tf''(t)dt
=1/4(xf'-积分f'dt)|(0,2)
=1/4(xf'(t)-f(t))|(0,2)
=1/4(2f'(2)-0f(0)-f(2)+f(0))=1/4(4-4+1)=1/4