- #1

Suraj M

Gold Member

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## Homework Statement

While integrating by parts( by the formula) why don't we consider the contant of integration for every integral in the equation.

## Homework Equations

$$∫uv = u∫v - ∫ ∫v . d/dx(u) $$

## The Attempt at a Solution

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example.

$$∫x \sin(x) dx = ?? $$

this is can be done like this

$$ x ∫ \sin(x) - ∫ ∫ \sin(x) .1 $$

$$ ⇒ -x \cos(x) + \sin(x) + c$$

why not like this..??

$$ ⇒ x( - \cos(x) +c₁ ) +\sin(x) +c₂$$

in this case the two constants don't add up to give one constant, it give s a new ##c_1x## term