Решебник по алгебре 11 класс Никольский Параграф 6. Первообразная и интеграл Задание 24

\[\boxed{\mathbf{24}.}\]

\[\textbf{а)}\ \int_{}^{}{x\cos x\text{dx}} =\]

\[= x\sin x - \int_{}^{}{\sin x\text{dx}} + C =\]

\[= x\sin x + \cos x + C.\]

\[\textbf{б)}\ \int_{}^{}\frac{\text{xdx}}{\text{co}s^{2}x} =\]

\[= x\ tg\ x - \int_{}^{}\text{tg\ x\ dx} + C =\]

\[= x\ tgx + \ln\left| \cos x \right| + C.\]

\[\textbf{в)}\ \int_{}^{}\frac{\text{xdx}}{\text{si}n^{2}x} =\]

\[= - x\ ctg\ x + \int_{}^{}\text{ctgx\ dx} + C =\]

\[= - x\ ctg\ x + \ln\left| \sin x \right| + C.\]

\[\textbf{г)}\ \int_{}^{}{x\sqrt{x - 7}\text{dx}} =\]

\[= \frac{2}{3}x(x - 7)^{\frac{3}{2}} - \frac{4(x - 7)^{\frac{5}{2}}}{15} + C =\]