Question

tính tích phân 

a) \(\int\limits^2_1\left(3x^2-\dfrac{2}{x}\right)dx\)

b) \(\int\limits^3_1\left(2x+\dfrac{1}{x^2}\right)dx\)

Answer 1

a: \(\int\left(3x^2-\dfrac{2}{x}\right)dx=3\cdot\dfrac{1}{3}x^3-2ln\left|x\right|+C\)

\(=x^3-2\cdot ln\left|x\right|+C\)

\(\int_1^2\left(3x^2-\dfrac{2}{x}\right)dx\)

\(\)\(=2^3-2\cdot ln\left|2\right|+C-\left(1^3-2\cdot ln\left|1\right|+C\right)\)

\(=8-2ln\left|2\right|-1+2\cdot ln\left|1\right|=7-2ln\left|2\right|\)

b: \(\int\left(2x+\dfrac{1}{x^2}\right)dx=2\cdot\dfrac{1}{2}x^2-\dfrac{1}{x}+C\)

\(=x^2-\dfrac{1}{x}+C\)

\(\int_1^3\left(2x+\dfrac{1}{x^2}\right)dx\)

\(=\left(3^2-\dfrac{1}{3}+C\right)-\left(1^2-\dfrac{1}{1}+C\right)\)

\(=9-\dfrac{1}{3}-1+1=\dfrac{26}{3}\)