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Evaluate the following definite integrals int_1^2 (1/x - 1/(2x^2)) e^(2x) dx

Answer»

SOLUTION :`int_1^2(1/x -1/(2X^2)) e^(2x) DX`
=`int_1^2 1/x e^(2x) dx - int_1^2 1/(2x^2) e^(2x) dx`
`[1/x (e^(2x))/2]_1^2 - int_1^2 -1/x^2 e^(2x)/2 dx - int_1^2 1/(2x^2) e^(2x) dx`
=`1/2 [e^4/2 -e^2/1] = (e^4-2e^2)/4 = (e^2(e^2-2))/4`


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