Question

uma primitiva para f(x)=4x^3-3cos(3x)

Answer 1

Olá


$\displaystyle\mathsf{\int 4x^3-3cos(3x)dx}\\\\\\\\\mathsf{4\int x^3-3\int cos(3x)dx}$


Propriedades:

$\displaystyle\boxed{\mathsf{\int x^pdx~=~ \frac{x^{p+1}}{p+1}+C }}\\\\\\\\\displaystyle\boxed{\mathsf{\int cos(\delta x)dx~=~ \frac{sen(\delta x)}{\delta}+C }}\qquad\qquad\qquad\mathsf{\delta \in \Re}$


Usando essas propriedades


$\displaystyle\mathsf{4\cdot \frac{x^{3+1}}{3+1}~ -~3\cdot \frac{sen(3x)}{3}+C }\\\\\\\mathsf{\diagup\!\!\!\!4\cdot \frac{x^{4}}{\diagup\!\!\!\!4}~ -~\diagup\!\!\!\!3\cdot \frac{sen(3x)}{\diagup\!\!\!\!3}+C }\\\\\\\boxed{\boxed{\mathsf{x^4-sen(3x)+C}}}$