Question

solve ∫ x³+3x+4*dx/√x

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{I}=\int \left[\frac{x^3+3x+4}{\sqrt{x}}\right]dx \\ \mathrm{I}=\int \left[\frac{x^3}{\sqrt{x}}+\frac{3x}{\sqrt{x}}+\frac{4}{\sqrt{x}}\right]dx \\ \mathrm{I}=\int \left[\frac{x^3}{x^{1/2}}+\frac{3x}{x^{1/2}}+4x^{-\frac{1}{2}}\right] \\ \mathrm{I}=\int \left[x^{5/2}+3x^{1/2}+4x^{-1/2}\right] \\ \mathrm{I}=\frac{2}{7}{x}^{7/2}+3\times \frac{2}{3}{x}^{3/2}+4\times 2x^{1/2}+\mathrm{C} \\ \mathrm{I}=\frac{2}{7}{x}^{7/2}+2x^{3/2}+8x^{1/2}+\mathrm{C} \end{gathered}$$