求不定积分∫1/sin^2(3x+4)dx ∫1/cos^2(6x^2+2)dx
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求不定积分∫1/sin^2(3x+4)dx ∫1/cos^2(6x^2+2)dx
∫3ln^2x+6lnx+7/xdx
∫e^x/√1-e^xdx
∫3ln^2x+6lnx+7/xdx
∫e^x/√1-e^xdx
1.∫1/sin^2(3x+4)dx
=1/3∫1/sin^2(3x+4)d(3x+4)
=-1/3cot(3x+4)+C
2.∫1/cos^2(6x+2)dx
=1/6∫1/cos^2(6x+2)d(6x+2)
=1/6tan(6x+2)+C
3.∫(3ln^2x+6lnx+7/x)dx
=3xln^2(x)-6∫lnxdx+6∫lnxdx+7ln|x|+C
=3xln^2(x) +7ln|x|+C
4.∫e^x/√1-e^xdx
=-∫(1-e^x)^(-1/2)d(1-e^x)
=-2(1-e^x)^(1/2)+C
=1/3∫1/sin^2(3x+4)d(3x+4)
=-1/3cot(3x+4)+C
2.∫1/cos^2(6x+2)dx
=1/6∫1/cos^2(6x+2)d(6x+2)
=1/6tan(6x+2)+C
3.∫(3ln^2x+6lnx+7/x)dx
=3xln^2(x)-6∫lnxdx+6∫lnxdx+7ln|x|+C
=3xln^2(x) +7ln|x|+C
4.∫e^x/√1-e^xdx
=-∫(1-e^x)^(-1/2)d(1-e^x)
=-2(1-e^x)^(1/2)+C
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