Question

Int (x+a)power3/√x dx?

Answer 1

`I=2/7x^(7/2)+2a^3x^(1/2)+6/5ax^(5/2)+2a^2x^(3/2)+c`

Explanation:

Here,

`I=int(x+a)^3/sqrtxdx`

`=int(x^3+a^3+3x^2a+3xa^2)/(x^(1/2))dx`

#=int(x^3/x^(1/2)+a^3/x^(1/2)+(3x^2a)/x^(1/2)+ (3xa^2)/x^(1/2))dx#

`=int(x^(3-1/2)+a^3x^(-1/2)+3ax^(2-1/2)+3a^2x^(1-1/2))dx`

`=int(x^(5/2)+a^3x^(-1/2)+3ax^(3/2)+3a^2x^(1/2))dx`

#=x^(5/2+1)/(5/2+1)+a^3x^(-1/2+1)/(-1/2+1)+3ax^(3/2+1)/(3/2+1 )+3a^2x^(1/2+1)/(1/2+1)+c#

#=x^(7/2)/(7/2)+a^3x^(1/2)/(1/2)+3ax^(5/2)/(5/2)+3a^2x^(3/2)/(3/ 2)+c#

#= (2x^(7/2))/7+2a^3x^(1/2)/(1)+6ax^(5/2)/(5)+2a^2x^(3/2)/(1)+c#

`=2/7x^(7/2)+2a^3x^(1/2)+6/5ax^(5/2)+2a^2x^(3/2)+c`

Note:

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