Tính nguyên hàm \(\int {\dfrac{{{{\left( {3\ln x +...

B

- Hướng dẫn giải

Ta có:

\(\begin{array}{l}\int {\dfrac{{{{\left( {3\ln x + 2} \right)}^4}}}{x}\,dx} \\ = \int {\left( {{{\left( {3\ln x + 2} \right)}^4}} \right)} \,d\left( {\ln x} \right)\\ = \dfrac{1}{3}\int {\left( {{{\left( {3\ln x + 2} \right)}^4}} \right)} \,d\left( {3\ln x + 2} \right)\\ = \dfrac{1}{3}.\dfrac{{{{\left( {3\ln 2 + 2} \right)}^5}}}{5} = \dfrac{{{{\left( {3\ln 2 + 2} \right)}^5}}}{{15}} + C.\end{array}\)