The integral ∫ 1 ( x - 1 ) 3 ( x + 2 ) 5 4   d x is equal to : (where C is a constant of integration)

Question

The integral &#8747; 1 ( x - 1 ) 3 ( x + 2 ) 5 4 &#160; d x is equal to : (where C is a constant of integration)

Aicharya · Accepted Answer

I = &#8747; d x ( x - 1 ) 3 ( x + 2 ) 5 4 I = &#8747; d x ( x - 1 ) 3 4 ( x + 2 ) 5 4 I = &#8747; d x ( x - 1 ) 2 x + 2 x - 1 5 4 Let x + 2 x - 1 &#160; = t Differentiate on both sides x - 1 - x + 2 x - 1 2 . d x &#160; = &#160; d t &#8658; d x x - 1 2 &#160; = &#160; - d t 3 I = - 1 3 &#8747; d t t 5 4 = &#160; - 1 3 t - 5 4 + 1 1 - 5 4 + C = 4 3 t - 1 4 + C = 4 3 1 t 1 4 + C = &#160; 4 3 x - 1 x + 2 1 4 + C

The integral ∫ 1 ( x - 1 ) 3 ( x + 2 ) 5 4   d x is equal to : (where C is a constant of…

Solution

The integral &#8747; 1 ( x - 1 ) 3 ( x + 2 ) 5 4 &#160; d x is equal to : (where C is a constant of…

Solution

The integral ∫ 1 ( x - 1 ) 3 ( x + 2 ) 5 4 d x is equal to : (where C is a constant of…