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Question
Solve the following : `int_1^2 e^(2x) (1/x - 1/(2x^2))*dx`
Solution
Let I = `int_1^2 e^(2x) (1/x - 1/(2x^2))*dx`
= `int_1^2 e^(2x)* (1)/xdx - int_1^2 e^(2x)* (1)/(2x^2)dx`
= `[(1)/x inte^(2x)*dx]_1^2 - int_1^2[d/dx(1/x)int e^(2x)*dx]dx - (1)/(2)`
= `[1/x* (e^(2x))/(2)]_1^2 - int_1^2(-1/x^2)*( e^(2x))/(2)dx - (1)/(2) int_1^2 e^(2x) 1/x^2*dx`
= `(1/4 e^4 - e^2/2) + (1)/(2) int_1^2 e^(2x)* (1)/x^2dx - (1)/(2) int_1^2 e^(2x)* (1)/x^2dx`
∴ I = `e^4/(4) - e^2/(2)`.
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