x^3 * (1+x^2)^1/2的積分值

Question

x^3 * (1+x^2)^1/2的不定積分值

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Answer 1

最佳解答

x^3 * (1+x^2)^1/2的積分值

u=1+x^2, du=2xdx

sx^3 * (1+x^2)^(1/2)dx

=(1/2)s x^2((1+x^2)^(1/2)*2x dx

=(1/2)s (u-1)u^(1/2)du

=(1/2)s u^(3/2)- u^(1/2)du

=(1/5)u^(5/2)-(1/3)u^(3/2)+C

=(1/5) (1+x^2) ^ (5/2) -(1/3) (1+x^2) ^(3/2)+C