Question

1 -A Integral de ( 3x + 7 dx ) é :

2-resolvendo a integral indefinida $\int\limits$($\int\limits x^{2}$-x)dx,obteremos qual função?

Answer 1

Para resolver este tipo de integrales simplemente debes tener en consideración dos cosas:

1) 
                               $\int x^n dx = \frac{x^{n+1}}{n+1}+C$

2)
                       $\int\lambda_1f(x)+\lambda_2g(x)\; dx=\lambda_1\int f(x)\; dx+\lambda_2\int g(x)\; dx$

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Entonces:
1.
$\displaystyle \int 3x+7 \;dx =3\int x \,dx + 7\int dx\\ \\ \\ \boxed{\int 3x+7 \;dx =\frac{3}{2}x^2+7x+C}$

2.
$\displaystyle \int x^2-x\;dx=\int x^2\;dx-\int x\;dx\\ \\ \\ \boxed{\int x^2-x\;dx=\frac{x^3}{3}-\frac{x^2}{2}+C}$

Answer 2

1)

$\boxed{\boxed{\mathsf{\int[3x+7]dx=\dfrac{3}{2}{x}^{2}+7x+C}}}$

2)

$\boxed{\boxed{\mathsf{\int[{x}^{2}-x]dx=\dfrac{1}{3}{x}^{3}-\dfrac{1}{2}{x}^{2}+C}}}$