Знайдіть невизначений інтеграл методом заміни змінної. Created by sbeznew197. matematika-ru

Ответ:Пошаговое объяснение:13)14)15)16)17)

Знайдіть невизначений інтеграл методом заміни змінної...

sbeznew197 @sbeznew197

August 2022 1 7 Report

Знайдіть невизначений інтеграл методом
заміни змінної

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pushpull

Ответ:

Пошаговое объяснение:

13)

$\int\limits\frac{8x^2}{(2x^3+1)^{11} } {} \, dx = 8\int\limits\frac{8x^2}{(2x^3+1)^{11} } {} \, dx = \left[\begin{array}{ccc}u=2x^3+1\\du = 6x^2dx\\\end{array}\right] =$

$= \frac{3}{4} \int\limits\frac{1}{u^{11} } {} \, dx = -\frac{2}{15u^{10} } + C = - \frac{2}{15(2x^3 +1)^{10} }$

14)

$\int\limits9(9x^{3}-6 )^{6} {x^{2} } \, dx = 9\int\limits {(9x^{3}-6 )^{6} {x^{2} }} \, dx =\left[\begin{array}{ccc}u= 9x^{3}-6} \\du=27x^{2}dx \\\end{array}\right] =$

$=\frac{1}{3}\int\limits {u^{6} } \, du } = \frac{u^{7} }{21} +C = \frac{(9x^3-6)^{7} }{21} +C$

15)

$\int\limits{\frac{4x^{3} }{(5x^{4} -2)^{5} } } \, dx = 4\int\limits {\frac{4x^{3} }{(5x^{4} -2)^{5} } } \, dx = \left[\begin{array}{ccc}u=5x^{4} -2\\du = 20x^{3} dx\\\end{array}\right] =$

$\frac{1}{5} \int\limits {\frac{1}{u^{4} } } \, du = -\frac{1}{20u^{4} } +C = -\frac{1}{20(5x^{4} -2)^{4} } +C$

16)

$\int\limits {14(5x^{4}-3 )^{3} x^{3} } \, dx = 14\int\limits {(5x^{4}-3 )^{3} x^{3} } \, dx =\left[\begin{array}{ccc}u=5x^{4}-3 \\du = 20x^{3} dx\\7&8&9\end{array}\right] =$

$= \frac{7}{10}\int\limits {u^{3} } \, du } = \frac{7u^{4} }{40} +C = \frac{7}{40} (5x^{4}-3 )^{4} +C$

17)

$\int\limits\frac{3x^{4} }{(6x^{5}+7 )^{5} } \, dx = 3\int\limits\frac{x^{4} }{(6x^{5}+7 )^{5} } \, dx = \left[\begin{array}{ccc}u=6x^{5}+7 \\du = 30x^{4} dx\\\end{array}\right] =$

$=\frac{1}{10} \int\limits {\frac{1}{u^{5} } } \, du= -\frac{1}{40u^{4} } +C = -\frac{1}{40(6x^{5}+7 )^{4} } +C$

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