高等数学 不定积分 求解谢谢
2个回答
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(1)
∫(3^x)^3 dx
=∫3^(3x) dx
= 3^(3x)/(3ln3) + C
(2)
∫3^(-x)(2.3^x-3.2^x) dx
=∫(2- 3.(2/3)^x) dx
=2x - [3/ln(2/3)].(2/3)^x + C
(3)
∫(1-1/x^2)√(x√x) dx
=∫(1-1/x^2).x^(3/4) dx
=∫[x^(3/4) - x^(-5/4) ] dx
= (4/7)x^(7/4) + 4x^(-1/4) + C
(4)
∫[3/(1+x^2)- 2/√(1-x^2)] dx
=3arctanx -2arcsinx + C
∫(3^x)^3 dx
=∫3^(3x) dx
= 3^(3x)/(3ln3) + C
(2)
∫3^(-x)(2.3^x-3.2^x) dx
=∫(2- 3.(2/3)^x) dx
=2x - [3/ln(2/3)].(2/3)^x + C
(3)
∫(1-1/x^2)√(x√x) dx
=∫(1-1/x^2).x^(3/4) dx
=∫[x^(3/4) - x^(-5/4) ] dx
= (4/7)x^(7/4) + 4x^(-1/4) + C
(4)
∫[3/(1+x^2)- 2/√(1-x^2)] dx
=3arctanx -2arcsinx + C
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