各章練習(xí)微積分五答案

設(shè)f(x)dxF(x)C，則sinxf(cosx)dx 設(shè)f(x)dxF(x)C，則f(sinx)cosxdx 設(shè)f(x)dxF(x)C，則xf'(x)dx

F(sinx)xf(x)F(x) 4.如果等式

f(x)exdxexC成立，則函數(shù)f(x)

ex若f(x)dxF(x)C，則exf(ex)dx 若ex是f(x)的一個(gè)原函數(shù)，則xf(x)dx 若f(x)ex，則f'(lnx)dx x

F(ex)(x1)ex1若f(x)dxx2C，則xf(1x2)dx 2(1x2)21如果 f(x)d[f(x)]2，且f(0)0，則f(x)

1x 3x21x3dx

(19

)2

x2ln|x1|Cf(x21)

xx2

，且f[(x)]lnx，則(x)dx 設(shè)f(lnx)1x（x0，則f(x)

xex fxdxgx

gxdxD．g'xdx

fxCfx

反函 下列各式中等于fx的 A．df B．df C．f' D．fxdx'設(shè)f(x)dx

2x21C，則xf(2x21)dx 1 4

2x21 2x21

2x21212(2x1)214設(shè)導(dǎo)數(shù)g'(x)f'(x)，則下列各式中正確的 g(x)f g(x)f(x)

函數(shù) 2 sin2

C.sin2 D.2sin2１3xexdx 1

3

C．3ex

1lnB 12x B. c

12x

12x9.設(shè)

1xdxln(1xC，則f(

f(x)dx x x x

x 2在區(qū)間(a,b)內(nèi)，如果f'(x)g'(x)，則下列各式中一定成立的 f(x)C.f(x)dx'g(x)

f(x)g(x)D.f'(x)dxg'(x)若sin2x是f(x)的一個(gè)原函數(shù)，則xf(x)dx xsin2xcos2xC.xsin2x1cos2x2

xsin2xcos2xD.xsin2x1cos2x2設(shè)f(x)dxF(x)C在[a,b]上成立， f(x)在[a,b]上必連續(xù)，但不一定可 B.f(x)在[a,b]上必可C.F(x)在[a,b]上必連續(xù)，但不一定可 D.F(x)在[a,b]上必可不定積分sin2xdx 22A.2cos2x B.xsinx C.1(xsinx) D.12sin2x2 sin2x 設(shè)2 f(x)，則f(x)dx 1cos2x

sin2x

x23x.4

x

44x3 1lnx3x2x 1

xtan10xsec2

x

1sin3 sin5 cosx2cos3x1cos5x

2 ２

2

1x1x 14x

1arcsin2x2 arcsin

1x

10.

cotx2lnsinxx4x 44x99364x95 x22x lnxx22xx22xx2ax2a13.

x2a2 2

x2a2 lnx 21xarccos xarccosx x2sin

x2cosx2xsinx2cosxxcotxlnsinx

arcsin

1 21xarcsinx 1cosln exexexcos

1xcoslnxsinlnx2arctanex1exsinxcosx2 1ex1 ln 1e

1ex x

xx6 24lnx64

x x22x xtan1x26.

ln

1

xln1ex３28．1sin

tanxsecxx 29．

2 arctanx

lnx ln(lnx)

xlnx x2

x21 x ＝x 2

x(1x)33.

x2arctan1x

＝xarctanx1ln|12

2|1(arctanx)22

1

＝

1ex

1

2 xx

x

2x

11ex1ex2 x 1cos xtan22lncos2 (cosx2cos3x1cos5x)sinx2 23x ＝32x9x27ln3x 1cos3xcosx1x1sin2x 1lnx11lnx211arctanx(x1)(x21)lnxx1ln