Question

найти неопределенный интеграл ∫x · (1 + x)^4dx​

Answer 1

$\int x\cdot (1+x)^4\, dx=\int x\cdot (x^4+4x^3+6x^2+4x+1)\, dx=\\\\\\=\int (x^5+4x^4+6x^3+4x^2+x)\, dx=\dfrac{x^6}{6}+\dfrac{4x^5}{5}+\dfrac{6x^4}{4}+\dfrac{4x^3}{3}+\dfrac{x^2}{2}+C=\\\\\\=\dfrac{x^6}{6}+\dfrac{4x^5}{5}+\dfrac{3x^4}{2}+\dfrac{4x^3}{3}+\dfrac{x^2}{2}+C$