Question

求大神帮忙看下这几个高数题





Answer 1

x²=(x-1+1)²
=∫1/(x-1)^8+2/(x-1)^9+1/(x-1)^10d(x-1)
=-1/7(x-1)^7-1/4(x-1)^8-1/9(x-1)^9+C

追答

令u=√(1+e^x)，
dx=dln(u²-1)=2u/(u²-1)du
=∫2/(u²-1)du
=∫1/(u-1)-1/(u+1)du
=ln(u-1)-ln(u+1)+C
代入u还原

高次利用二倍角公式降次
=2∫(0.π/2)(cos2θ+1)²dθ
=∫(cos4θ+1)+4cos2θ+2dθ
=sin4θ/4+2sin2θ+3θ
=3π/2
学了牛顿-莱布尼茨公式更简单
=2*4*(3/4)*(1/2)*π/2=3π/2

Answer 2

！！！！！！！！

Answer 3

如图