Bài tập 1 trang 141 SGK Toán 12 NC

a)

\(\begin{array}{l}
\int {\left( {3{x^2} + \frac{x}{2}} \right)} dx\\
 = 3\int {{x^2}dx}  + \frac{1}{2}\int {xdx} \\
 = {x^3} + \frac{{{x^2}}}{4} + C
\end{array}\)

b)

\(\begin{array}{l}
\int {\left( {2{x^3} - 5x + 7} \right)} dx\\
 = 2\int {{x^3}dx}  - 5\int {xdx}  + 7\int {dx} \\
 = \frac{{{x^4}}}{2} - \frac{{5{x^2}}}{4} + 7x + C
\end{array}\)

c)

\(\begin{array}{l}
\int {\left( {\frac{1}{{{x^2}}} - {x^2} - \frac{1}{3}} \right)} dx\\
 = \int {{x^{ - 2}}dx}  - \int {{x^2}dx}  - \frac{1}{3}\int {dx} \\
 =  - \frac{1}{x} - \frac{{{x^3}}}{3} - \frac{x}{3} + C
\end{array}\)

d) \(\int {\left( {{x^{ - \frac{1}{3}}}} \right)} dx = \frac{{{x^{\frac{2}{3}}}}}{{\frac{2}{3}}} + C = \frac{3}{2}{x^{\frac{2}{3}}} + C\)

e) \(\int {{{10}^{2x}}} dx = \frac{{{{10}^{2x}}}}{{2.\ln 10}} + C\)

-- Mod Toán 12 HỌC247