Question

Calcule a integral indefinida

Answer 1

olá!!!

segue a resposta na imagem!!!


Bons estudos!!!

Answer 2

Olá


$\displaystyle \mathsf{\int x\cdot sen(3x^2-1)dx}$



Integrando pelo método da substituição 'udu'


$\displaystyle \mathsf{u=3x^2-1}\\\\\\\mathsf{du=6xdx}\qquad\qquad\Longrightarrow\qquad\mathsf{ \frac{1}{6}du=xdx }$



Substituindo na integral


$\displaystyle \mathsf{\int sen(u)\frac{1}{6}du}\\\\\\\mathsf{ \frac{1}{6}\mathsf{\int sen(u)du}\qquad\qquad\qquad\qquad\boxed{\mathsf{\int senx~dx=-cosx+c}}}\\\\\\\\\mathsf{= -\frac{1}{6}cos(u)+C }\\\\\\\mathsf{u=3x^2-1}\\\\\\\boxed{\boxed{\mathsf{=- \frac{1}{6} cos(3x^2-1)+C}}}$




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