`int (4x^3 + 3)/(x^4 + 3x) dx` Find the indefinite integral.

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lemjay eNotes educator| Certified Educator

`int (4x^3+3)/(x^4+3x)dx`

To solve, apply u-substitution method. So let:

`u= x^4+3x`

Then, differentiate it.

`du=(4x^3+3)dx`

Plug-in them to the integral. 

`int (4x^3+3)/(x^4+3x)dx`

`= int 1/(x^4+3x)* (4x^3+3)dx`

`=int1/udu`

Then, apply the integral formula  `int 1/xdx = ln|x| + C` .

`= ln|u| + C`

And, substitute back  `u=x^4+3x` .

`=ln |x^4+3x|+C`

 

Therefore,  `int (4x^3+3)/(x^4+3x)dx = ln|x^4+3x|+C` .

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