Question

intregration x³+4x¹/² dx

Answer 1

integration of x^3+4x^1/2dxis x^4/4+8/3x^3/2+c

Answer 2

your question is ------> $\int{(x^4+x^{1/2})}\,dx$

we know, $\int{x^n}\,dx=\left[\frac{x^{n+1}}{n+1}\right]+C$

now,
$\int{(x^4+x^{1/2})}\,dx\\\\\\=\int{x^4}\,dx+\int{x^{1/2}}\,dx\\\\\\=\left[\frac{x^{4+1}}{4+1}\right]+\left[\frac{x^{1/2+1}}{1/2+1}\right]+C\\\\\\=\frac{x^5}{5}+\frac{2}{3}x\sqrt{x}+C$