Question

Find the following integral: $\int \frac{x^3+3x+4}{\sqrt x}dx$

Answer 1

$\int \frac{x^3+3x+4}{\sqrt x}dx$

= $\int \bigg(x^{\frac{5}{2}}+3x^{\frac{1}{2}}+4x^{-\frac{1}{2}}\bigg)dx$

=$\frac{x^{\frac{7}{2}}}{\frac{7}{2}}+\frac{3\bigg(x^{\frac{3}{2}}\bigg)}{\frac{3}{2}}+\frac{4\bigg(x^{\frac{1}{2}}\bigg)}{\frac{1}{2}}+C$

=$\frac{2}{7}x^{\frac{7}{2}}+2x^{\frac{3}{2}}+8x^{\frac{1}{2}}+C$

= $\frac{2}{7}x^{\frac{7}{2}}+2x^{\frac{3}{2}}+8\sqrt x+C$