Question

integral x.cos(5x^2+π)dx

Answer 1

Calcular a integral indefinida

     $\displaystyle\int x\cdot \cos(5x^2+\pi)\,dx\\\\\\ =\int \frac{1}{10}\cdot 10x\cdot \cos(5x^2+\pi)\,dx\\\\\\ =\frac{1}{10}\int \cos(5x^2+\pi)\cdot 10x\,dx$


Faça uma substituição:

     $5x^2+\pi=u\quad\Rightarrow\quad 10x\,dx=du$


e a integral fica

     $\displaystyle=\frac{1}{10}\int \cos(u)\,du\\\\\\ =\frac{1}{10}\cdot \mathrm{sen}(u)+C$

     $=\dfrac{1}{10}\,\mathrm{sen}(5x^2+\pi)+C\quad\longleftarrow\quad\textsf{esta \'e a resposta}$


Bons estudos! :-)