Evaluate the integral. \int \frac{2x^{2}+7x-3}{x-2}dx

DofotheroU 2021-11-07 Answered
Evaluate the integral.
2x2+7x3x2dx
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Expert Answer

unessodopunsep
Answered 2021-11-08 Author has 105 answers
Given
The integral is 2x2+7x3x2dx
solution
2x2+7x3x2dx=2(x2)2+15(x2)+19x2dx
let u=x-2; du=dx
2x2+7x3x2dx=2u2+15u+19udu
=2u2udu+15uudu+19udu
=2udu+151du+191udu
=2u22+15u+19lnu+C
put u=x-2
2x2+7x3x2dx=(x2)2+15(x2)+19ln(x2)+C
=x24x+4+15x30+19ln(x2)+C
=x2+11x26+19ln(x2)+C
2x2+7x3x2dx=x2+11x+19ln(x2)+C   (C=C26)
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