The integral ∫ e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x   d x ,   x > 0 , is equal to (where c is a constant of integration)

Question

The integral &#8747; e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x &#160; d x , &#160; x &#62; 0 , is equal to (where c is a constant of integration)

Aicharya · Accepted Answer

&#8747; e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x d x , x &#62; 0 = &#8747; 2 x 3 + 5 2 x 2 x 4 + 5 x 3 - 7 x 2 d x = &#8747; 4 x 2 2 x + 5 x 2 x 2 + 5 x - 7 d x = 4 &#8747; d x 2 + 5 x - 7 x 2 + 5 x - 7 = 4 log e x 2 + 5 x - 7 + c

The integral ∫ e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x   d x …

Solution

The integral &#8747; e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x &#160; d x …

Solution

The integral ∫ e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x d x …