1、习题课习题课- 1 -第四章第四章不定积分不定积分第四章习题课1.)43(2dxxx+一 计算下列不定积分+= dxxx23434)43(原式解+=43)43(91xxd+ )43()43(1942xdx|43|ln91+= xCx+)43(94习题课习题课- 2 -第四章第四章不定积分不定积分2112cosdxx x解原式11cos dx x=1sin Cx=+ )1(32xxeedx解原式2221(1 )xxxxeedxee+ =+xedx= 21xxedxe+()xed x= 211()xxdee+arctanxxeeC= +习题课习题课- 3 -第四章第四章不定积分不定积分4sin c
2、os41sinxxdxx+解原式4sinsin1sinxdxx=+2411sin21sindxx=+21arctansin2x C= +3sin cos5sin cosx xdxx x+解原式13(sin cos ) (sin cos )x xd x x= 233(sin cos )2x xC= +习题课习题课- 4 -第四章第四章不定积分不定积分7ln ln(ln )dxx xx226tan1 .1xdxxx+解原 式2221(1)tan 121dxxx+=+22tan 1 1xd x= +2ln |sec 1 |x C= +解原式1lnln ln(ln )dxxx=1ln(ln )ln(l
3、n )dxx=ln |ln(ln )|x C= +习题课习题课- 5 -第四章第四章不定积分不定积分2arcsin21081xdxx解原式2arcsin10 arcsinxdx=2arcsin110 (2arcsin )2xdx=2arcsin1102ln10xC= +arctan9(1 )xdxxx+解原式arctan21xdxx=+2 arctan arctanxdx=2arctan xC= +习题课习题课- 6 -第四章第四章不定积分不定积分2310 .94xxxxdx解原式= dxxx23232)(1)(=xxd )()(113ln2ln132232Cxx+=|)(1|)(1|ln)3
4、ln2(ln213232Cxxxx+=2323ln)3ln2(ln21习题课习题课- 7 -第四章第四章不定积分不定积分sin121sinxdxx+1cos11sinxdxx x+解原式1(sin)sindx xx x=+ln | sin |x xC=+解原式sin (1 sin )(1sin)(1sin)x xdxxx=+22sin sincosx xdxx=2(sec 1)xdx2coscosdxx=tan x xC +1cos x=习题课习题课- 8 -第四章第四章不定积分不定积分13 设2() ,xf xe= 求() ()f xf xdx解() ()f xf xdx() ()f xdf
5、 x =21()2fx C= +2()xf xe=2() 2xf xxe =221() () 2 2xf x f x dx xe C= +2222xxe C= +习题课习题课- 9 -第四章第四章不定积分不定积分解= dxxfxfxfxfxf)()()()()(322原式.)()()()()(1432dxxfxfxfxfxf= dxxfxfxfxfxfxf)()()()()()(22= )()()()(xfxfdxfxf.)()(212Cxfxf+=习题课习题课- 10 -第四章第四章不定积分不定积分二 计算下列不定积分112dxx+2,x t=令2,2tx = dx tdt=解原式1tdtt=+1dtdtt=+ ln |1 |ttC= + +2ln(12)x xC=+ +
