`int (-3x)/(x^2+3)^(3/2) dx` Find the indefinite integral

`int(-3x)/(x^2+3)^(3/2)dx`

Take the constant out,

`=-3intx/(x^2+3)^(3/2)dx`

Apply integral substitution:`u=x^2+3`

`=>du=2xdx`

`=-3int1/(u)^(3/2)(du)/2`

Take the constant out,

`=-3/2int1/u^(3/2)du`

`=-3/2intu^(-3/2)du`

Apply the power rule,`intx^adx=x^(a+1)/(a+1), a!=-1`

`=-3/2(u^(-3/2+1))/(-3/2+1)`

`=-3/2u^(-1/2)/(-1/2)`

`=-3/2(-2/1)u^(-1/2)`

`=3/u^(1/2)`

Substitute back `u=x^2+3`

`=3/(x^2+3)^(1/2)`

Add a constant C to the solution,

`=3/sqrt(x^2+3)+C`

Comments

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