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4x-e-3x-dx-

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Question Number 22210 by cmaxamuud98 @gmail.com last updated on 13/Oct/17
∫((4x)/e^(3x) )dx
∫4xe3xdx
Answered by ajfour last updated on 13/Oct/17
=4∫xe^(−3x) dx =4{x∫e^(−3x) dx−∫(∫e^(−3x) dx)dx} =4{x(−(1/3)e^(−3x) +c_1 )−∫((e^(−3x) /(−3))+c_1 )dx} =4{−(x/3)xe^(−3x) +c_1 x−(1/3)((e^(−3x) /(−3))+c_1 ) −c_1 x+c_2 } =−(4/3)xe^(−3x) +(4/9)e^(−3x) +c =(4/9)e^(−3x) (1−3x)+c .
=4∫xe−3xdx=4{x∫e−3xdx−∫(∫e−3xdx)dx}=4{x(−13e−3x+c1)−∫(e−3x−3+c1)dx}=4{−x3xe−3x+c1x−13(e−3x−3+c1)−c1x+c2}=−43xe−3x+49e−3x+c=49e−3x(1−3x)+c.

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