r44,x>0x +4

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Solution

The integral of the function is given as,

∫ x x+4 dx(1)

Consider, x+4=t.

Differentiate with respect to x.

x+4=t dx=dt

Substitute dx=dt in equation (1) and then integrate.

∫ x x+4 dx= ∫ t−4 t = ∫ t t dt−4 ∫ 1 t dt = ∫ t dt−4 ∫ ( t ) − 1 2 dt

Integrate the equation and simplify.

∫ x x+4 dx = ∫ t dt−4 ∫ ( t ) − 1 2 dt =( t 3 2 3 2 )−4( t 1 2 1 2 )+C

Substitute x+4=t in the above equation.

∫ x x+4 dx= 2 3 ( t ) 3 2 −8 ( t ) 1 2 +C = 2 3 ( x+4 ) 3 2 −8 ( x+4 ) 1 2 +C

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