作业帮求下列不定积分?
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求下列不定积分?
求下列不定积分?
求下列不定积分?
原式=1/2∫x^2/(a^2+x^2)^(3/2)dx^2
=1/2∫(x^2+a^2-a^2)/(a^2+x^2)^(3/2)dx^2
=1/2∫[1/√(x^2+a^2)-a^2/(a^2+x^2)^(3/2)]dx^2
=√(x^2+a^2)+1/4*a^2/(a^2+x^2)^(1/2)+C
答：
∫ x³/(a²+x²)^(3/2) dx
=(1/2) ∫ (a²+x²-a²)/(a²+x²)^(3/2) d(x²+a²)
=(1/2) ∫ 1/(a²+x²)^(1/2) -a²/(a²+x²)^(3/2) d(...
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答：
∫ x³/(a²+x²)^(3/2) dx
=(1/2) ∫ (a²+x²-a²)/(a²+x²)^(3/2) d(x²+a²)
=(1/2) ∫ 1/(a²+x²)^(1/2) -a²/(a²+x²)^(3/2) d(a²+x²)
=(a²+x²)^(1/2) -(a²/2)*(-1/2)*(a²+x²)^(-1/2)+C
=√(a²+x²)+a²/[4√(a²+x²)]+C
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