समाकलन `int((1+x)^(3))/(sqrt(x))dx` का मान ज्ञात कीजिए

Options

A. `2sqrt(x)-2x^((3)/(2))-(6)/(5)x^((5)/(2))+(2)/(7) x^((7)/(2))+C`
B. `2sqrt(x)+2x^((3)/(2))+(6)/(5)x^((5)/(2))+(2)/(7) x^((7)/(2))+C`
C. `2sqrt(x)-2x^((3)/(2))-(6)/(5)x^((5)/(2))-(2)/(7) x^((7)/(2))+C`
D. इनमे से कोई नहीं

Answer

B

Explanation

`int ((1+x)^(3))/(sqrt(x))dx=int(1_3x+3x^(2)+x^(3))/(sqrt(x))dx`
`=int x^((-1)/(2))dx+3intx^((1)/(2))dx+3int x^((3)/(2))dx+intx^((5)/(x^(2)))dx`
`=(x^((1)/(2)))/((1)/(2))+3*(x^((3)/(2)))/((3)/(2))+3*(x^((5)/(2)))/((5)/(2))+(x^((7)/(2)))/((7)/(2))+C`
`=2sqrt(x)+2x^((3)/(2))+(6)/(5)x^((5)/(2))+(2)/(7)x^((7)/(2))+C`