`int x^4 - (1/2)x^3 + (1/4)x - 2 dx` Find the general indefinite integral.

Textbook Question

Chapter 5, 5.4 - Problem 7 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`int (x^4-1/2x^3+1/4x-2)dx`

To evaluate this integral, apply the formulas

`int x^n dx=x^(n+1)/(n+1) +C`   and  `int adx = ax + C` .

 

`int (x^4-1/2x^3+1/4x-2)dx`

`=x^5/5 - 1/2*x^4/4 + 1/4*x^2/2-2x + C`

`=x^5/5 - x^4/8 +x^2/8-2x+C`

 

Therefore, `int (x^4-1/2x^3+1/4x-2)dx = x^5/5 - x^4/8 + x^2/8 -2x + C` .

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