5 months ago
Q:

Enter a primitive function to F(x)=x^2+3x

Accepted Solution

A:

Solution variant #1.

Use the property of integral $\int{ f\left( x \right)\pmg\left( x \right) } \mathrm{d} x=\int{ f\left( x \right) } \mathrm{d} x\pm\int{ g\left( x \right) } \mathrm{d} x$
$\int{ {x}^{2} } \mathrm{d} x+\int{ 3x } \mathrm{d} x$
Use $\begin{array} { l }\int{ {x}^{n} } \mathrm{d} x=\frac{ {x}^{n+1} }{ n+1 },& n≠-1\end{array}$ to evaluate the integral
$\frac{ {x}^{3} }{ 3 }+\int{ 3x } \mathrm{d} x$
Evaluate the indefinite integral
$\frac{ {x}^{3} }{ 3 }+\frac{ 3{x}^{2} }{ 2 }$
Add the constant of integration $C \in ℝ$
$\begin{array} { l }\frac{ {x}^{3} }{ 3 }+\frac{ 3{x}^{2} }{ 2 }+C,& C \in ℝ\end{array}$