Question

Найти неопределенные интегралы а) б) в)

Answer 1

$\int{ \frac{sin3x}{4+cos3x} } \, dx = -\int{ \frac{1}{3(4+cos3x)} } \, d(cos3x+4) = -\frac{1}{3} ln(4+cos3x)+ C$

$\int {xsin5x} \, dx =- \frac{1}{5} \int {x} \, dcos5x =-\frac{1}{5}(xcos5x - \int {cos5x} \, dx)= \\\\=\frac{1}{25} sin5x- \frac{1}{5} xcos5x+C$

$\int { \frac{x^2+17x+20}{(x-3)(x+1)^2} } \, dx =\int {(- \frac{4}{x+1} - \frac{1}{(x+1)^2 }+ \frac{5}{x-3} ) } \, dx =\\\\=5ln|x-3|+ \frac{1}{x+1} -ln|x+1|$