Question

Eu am incercat cu schimbare de variabila dar n-am reusit sa-l duc la capat

Answer 1

[tex] \int\limits^4_1 {y^xlny} \, dy= \int\limits^4_1 {( \frac{y^{x+1}}{x+1})'\cdot lny } \, dy =\\ = \frac{y^{x+1}}{x+1}\cdot lny|_1^4- \frac{1}{x+1} \int\limits^4_1 {y^{x+1}} \cdot \frac{1}{y} \, dy =\\ = \frac{4^{x+1}}{x+1}\cdot ln4 - \frac{1}{x+1} \cdot \frac{y^{x+1}}{x+1}|_{1}^{4}=\\ = \frac{4^{x+1}}{x+1}\cdot ln4-\frac{1}{(x+1)^2}\cdot(4^{x+1}-1)[/tex]