\( \int \frac{(1+x)^{2}}{\sqrt{x}} d x \)

Question

find intergel :\( \int \frac{(1+x)^{2}}{\sqrt{x}} d x \)

Answer 1

∫\(\frac{(1+x^2)}{\sqrt x}dx=\int\frac{x^2+2x+1}{\sqrt x}dx\)

= ∫(x^3/2 + 2 x^1/2 + x^-1/2)dx

= 2/5 x^5/2 + 4/3 x^3/2 + 2x^1/2 + c (∵ ∫x^x dx \(=\frac{x^n+1}{n+1})\)