intregration x³+4x¹/² dx
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integration of x^3+4x^1/2dxis x^4/4+8/3x^3/2+c
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your question is ------> 
we know,![\int{x^n}\,dx=\left[\frac{x^{n+1}}{n+1}\right]+C](https://tex.z-dn.net/?f=%5Cint%7Bx%5En%7D%5C%2Cdx%3D%5Cleft%5B%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%5Cright%5D%2BC "\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](https://tex.z-dn.net/?f=%5Cint%7B%28x%5E4%2Bx%5E%7B1%2F2%7D%29%7D%5C%2Cdx%5C%5C%5C%5C%5C%5C%3D%5Cint%7Bx%5E4%7D%5C%2Cdx%2B%5Cint%7Bx%5E%7B1%2F2%7D%7D%5C%2Cdx%5C%5C%5C%5C%5C%5C%3D%5Cleft%5B%5Cfrac%7Bx%5E%7B4%2B1%7D%7D%7B4%2B1%7D%5Cright%5D%2B%5Cleft%5B%5Cfrac%7Bx%5E%7B1%2F2%2B1%7D%7D%7B1%2F2%2B1%7D%5Cright%5D%2BC%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7Bx%5E5%7D%7B5%7D%2B%5Cfrac%7B2%7D%7B3%7Dx%5Csqrt%7Bx%7D%2BC "\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")
we know,
now,
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