高等数学A上册习题解答 至微分中值定理(15)

华中师范大学专用

(10)

1

x(x+a)

dx,

(a=0)

-u=xn+a,K,du=nxn 1dx,

dx=

du

1

x(x+adx

=

)du

nu(u a)=1 na[1u a 1u]du=1u analn|u

|+C=1

ln|xn|+C. 1

x(xn+adx

=

)11

xn 1a[x xn+a]dx

=1aln|x| 1naln|xn+a|+C.(11)

sinxcos3x

1+cos2xdx

cos3= x

dcosx

==u=cos====x

=

u31du

=

+u[u

1+u u]du

=1

[ln(1+u2) u22]+C=1

[ln(1+cos2x) cos2x]+C. 2=1

2

[ln(2 sin2x)+sin2

x]+C15

(0.37)

(0.38)

(0.39)

(0.40)

):