求解不定积分2-6
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(2)
∫ 3/(x.√x) dx
=3∫ x^(-3/2) dx
=-6x^(-1/2) +C
=-6√x +C
(3)
∫ (5^x/7^x) dx
=∫ (5/7)^x dx
=(5/7)^x/ln(5/7) + C
(4)
∫ 2/(5x+3) dx
=(2/5)∫d(5x+3)/(5x+3)
=(2/5)ln|5x+3| +C
(5)
∫x^2.e^(x^3) dx
=(1/3)∫e^(x^3) dx^3
=(1/3)e^(x^3) +C
(6)
∫ xcos(2x^2+3) dx
=(1/2)∫ cos(2x^2+3) d(2x^2+3)
=(1/2)sin(2x^2+3) +C
∫ 3/(x.√x) dx
=3∫ x^(-3/2) dx
=-6x^(-1/2) +C
=-6√x +C
(3)
∫ (5^x/7^x) dx
=∫ (5/7)^x dx
=(5/7)^x/ln(5/7) + C
(4)
∫ 2/(5x+3) dx
=(2/5)∫d(5x+3)/(5x+3)
=(2/5)ln|5x+3| +C
(5)
∫x^2.e^(x^3) dx
=(1/3)∫e^(x^3) dx^3
=(1/3)e^(x^3) +C
(6)
∫ xcos(2x^2+3) dx
=(1/2)∫ cos(2x^2+3) d(2x^2+3)
=(1/2)sin(2x^2+3) +C
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