Question

Найти производную функции: y=7Sin(6x^5+7x^3+3x^2)
И
Вычислить интеграл по частям: ∫(7x+9)Sin7xdx

Answer 1

$[7sin(6x^5+7x^3+3x^2)]'=\ =7cos(6x^5+7x^3+3x^2)*(6x^5+7x^3+3x^2)'=\ =7cos(6x^5+7x^3+3x^2)*(30x^4+21x^2+6x)$
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$intlimits {(7x+9)sin7x} , dx = frac{1}{7} intlimits {7x*sin(7x)} , d(7x)+frac{9}{7}intlimits {sin(7x)} , d(7x) =\ =frac{1}{7} intlimits {t*sin(t)} , dt+frac{9}{7}intlimits {sin(t)} , dt =\ =frac{1}{7} intlimits {t} , d(-cos(t))-frac{9}{7}cos(t)=\ =-frac{1}{7}[tcos(t)- intlimits {cos(t)} , dt ]-frac{9}{7}cos(t)=\ =frac{1}{7}[tcos(t)-sin(t) ]-frac{9}{7}cos(t)+C, where t=7x$