∫e∧sinxcosxdx

瞿宰侄814∫xtanx∧2dx等于多少 -
翁残海15134599226 ______ ∫x(tanx)^2dx=∫x[(secx)^2-1]dx=∫x(secx)^2dx-∫xdx=∫xd(tanx)-(x^2)/2=-(x^2)/2+[xtanx-∫tanx dx]=-(x^2)/2+[xtanx+∫(1/cosx)d(cosx)=xtanx+ln|cosx|-(x^2)/2+C

瞿宰侄814∫xsin∧4(x)dx= ?急求 谢谢啦! -
翁残海15134599226 ______ ∫x(sinx)^4dx=(1/4)∫x(1-cos2x)^2dx=(1/4)∫[x-2xcos2x +x(cos2x)^2 ]dx=(1/8)∫[2x-4xcos2x +x(1+cos4x) ]dx=(1/8)∫[3x-4xcos2x +xcos4x ]dx=(1/8)[(3/2)x^2-∫ 4xcos2xdx +∫xcos4x dx ] consider ∫4xcos2xdx=2∫xdsin2x=2xsin2x - 2∫sin2x dx=2xsin2x +cos2x ...

瞿宰侄814∫(0,1)e∧(x∧2)dx与∫(0,1)e∧xdx的大小 -
翁残海15134599226 ______[答案] 前者大,被积函数前者的增长性比后者的大.画个图比较一下面积就好了.

瞿宰侄814∫e∧5t. dt -
翁残海15134599226 ______ ∫e^(5t)dt=(1/5)∫e^(5t)d(5t)=(1/5)e^(5t) +C

瞿宰侄814∫2xe∧x∧2dx等于多少 -
翁残海15134599226 ______ ∫2xe∧x∧2dx =∫e^x^2d(x^2) =e^x^2+C

瞿宰侄814∫ (lnx)∧2dx怎样求 -
翁残海15134599226 ______ ∫(lnx)^2dx=x(lnx)^2 - 2∫lnx dx=x(lnx)^2 - 2xlnx +2∫dx=x(lnx)^2 - 2xlnx +2x + C

瞿宰侄814∫(0→∞)x*e∧xdx怎么积分? -
翁残海15134599226 ______[答案] 原题是发散的.改一下: ∫(0→∞)x*e∧(-x)dx=-∫(0→∞)xde^(-x) =-xe^(-x)|_0^∞+∫(0→∞)e^(-x)dx =0-e^(-x)||_0^∞=1.

瞿宰侄814∫e∧tanx dx怎么算呢? -
翁残海15134599226 ______ 结果不是初等函数,算不了.

瞿宰侄814∫(1→0)e∧4xdx -
翁残海15134599226 ______ ∫e^4xdx=1/4*∫e^4x d(4x)=1/4*e^4x ∴∫(1→0)e∧4xdx=1/4*e^4-1/4*e^0=1/4(e^4-1)

瞿宰侄814d/dx∫e∧t(t - x)dt等于什么 -
翁残海15134599226 ______ 积分得到∫e^t (t-x)dt=∫(t-x) d(e^t)=(t-x) *e^t -∫e^t dt=(t-x) *e^t -e^t +C 再对x 求导就得到 -e^t