Calculate: integral of 5+(2)/(3)x^{(5)/(2)}+2x^3 x

Expression: $\int{ 5+\frac{ 2 }{ 3 }{x}^{\frac{ 5 }{ 2 }}+2{x}^{3} } \mathrm{d} x$

Use the property of integral $\int{ f\left( x \right)\pmg\left( x \right) } \mathrm{d} x=\int{ f\left( x \right) } \mathrm{d} x\pm\int{ g\left( x \right) } \mathrm{d} x$

$\int{ 5 } \mathrm{d} x+\int{ \frac{ 2 }{ 3 }{x}^{\frac{ 5 }{ 2 }} } \mathrm{d} x+\int{ 2{x}^{3} } \mathrm{d} x$

Use $\int{ a } \mathrm{d} x=a \times x$ to evaluate the integral

$5x+\int{ \frac{ 2 }{ 3 }{x}^{\frac{ 5 }{ 2 }} } \mathrm{d} x+\int{ 2{x}^{3} } \mathrm{d} x$

Evaluate the indefinite integral

$5x+\frac{ 4{x}^{3}\sqrt{ x } }{ 21 }+\int{ 2{x}^{3} } \mathrm{d} x$

Evaluate the indefinite integral

$5x+\frac{ 4{x}^{3}\sqrt{ x } }{ 21 }+\frac{ {x}^{4} }{ 2 }$

Add the constant of integration $C \in ℝ$

$\begin{array} { l }5x+\frac{ 4{x}^{3}\sqrt{ x } }{ 21 }+\frac{ {x}^{4} }{ 2 }+C,& C \in ℝ\end{array}$