Question

Ai làm ơn giúp với 

Answer 1

\(\int_2^5\dfrac{x}{(x-1)(x+2)}dx=\dfrac{1}{3}\int_2^5\dfrac{3x}{(x-1)(x+2)}dx\)

\(=\dfrac{1}{3}\int_2^5[\dfrac{1}{(x-1)}+\dfrac{2}{(x+2)}]dx\)

\(=\dfrac{1}{3}\int_2^5\dfrac{1}{(x-1)}dx+\dfrac{2}{3}\int_2^5\dfrac{1}{(x+2)}dx\)

\(=\dfrac{1}{3}.\ln(x-1)|_2^5+\dfrac{2}{3}.\ln(x+2)|_2^5\)

\(=...\)