Question

Integrala din x^4 (1-x^5)^5

Answer 1

$\displaystyle \int \displaysyle x^4(1-x^5)^5\, dx =\\ \\=-\dfrac{1}{5}\int -5x^4(1-x^5)^5 \, dx\\ \\= -\dfrac{1}{5}\int (1-x^5)'(1-x^5)^5\,dx\\ \\ = -\dfrac{(1-x^5)^6}{5\cdot 6}+C \\ \\ = -\dfrac{(1-x^5)^6}{30}+C$