Question

Найти интегралы ( 1-3 хотябы). Минут за .

Answer 1

$4)\ \ \int \dfrac{x^5\, dx}{x^6+7}=\dfrac{1}{6}\int \dfrac{d(x^6+7)}{x^6+7}=ln|x^6+7|+C\\\\\\5)\ \ \int (x^2+4)^2\cdot x\, dx=\dfrac{1}{2}\int (x^2+4)^2\cdot d(x^2+4)=\dfrac{1}{2}\cdot \dfrac{(x^2+4)^3}{3}+C\\\\\\1)\ \ \int cos^5x\cdot sinx\, dx=-\int cos^5x\cdot d(cosx)=-\dfrac{cos^6x}{6}+C\\\\\\2)\ \ \int x\cdot e^{3x^2-2}\, dx=\dfrac{1}{6}\int e^{3x^2-2}\cdot d(3x^2-2)=\dfrac{1}{6}\cdot e^{3x^2-2} +C$