Задача 57154 ...
Условие
Решение
[m] ∫ (10e^{x}+e^{10x}+8)dx=10\cdot∫ e^{x}dx+∫ e^{10x}dx+ ∫ 8\cdot dx=[/m]
[m]=10\cdot e^{x}+∫ e^{10x}dx+8 \cdot∫ dx=[/m]
[m]=10\cdot e^{x}+\frac{1}{10}e^{10x}+8 x+C[/m]
2.
[m] ∫ (cosx-12^{x}+12x^{3})dx=∫ cosx dx - ∫ 12 ^{x}dx+12\cdot ∫ x^{3}dx=sinx-\frac{12^{x}}{ln12}+12\cdot \frac{x^4}{4}+C=[/m]
[m]=sinx-\frac{12^{x}}{ln12}+3\cdot x^4+C[/m]
3.
[m] ∫ (\frac{14}{x}+2sinx+14)dx=14\cdot∫ \frac{1}{x} dx +2\cdot ∫ sinxdx+12∫ dx=14\cdot ln|x|+2\cdot (-cosx)+14x+C=[/m]
[m]=14\cdot ln|x|-2\cdot cosx+14x+C[/m]
4.
[m] ∫ (22^{x}+e^{22x}+\frac{1}{22}e^{x})dx=∫22^{x}dx + ∫ e ^{22x}dx+\frac{1}{22}\cdot ∫ e^{x}dx=\frac{22^{x}}{ln22}+\frac{1}{22}\cdot e^{22x}+\frac{1}{22}e^{x}+C[/m]
5.
[m] ∫ (x^{100}+x^{78}-x^{12}+12x)dx=∫ x^{100}dx+ ∫ x^{78}dx- ∫ x^{12}fx+12\cdot ∫ xdx=\frac{x^{101}}{101}+\frac{x^{79}}{79}-\frac{x^{13}}{13}+12\cdot \frac{x^{2}}{2}+C=[/m][m]\frac{x^{101}}{101}+\frac{x^{79}}{79}-\frac{x^{13}}{13}+6\cdot x^{2}+C[/m]
