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Indefinite Integral - Evaluate Please.?
Evaluate the indefinite integral
((2/x^4)+(4/15x))dx.
The answer is not -2/(3 x^3)+(4ln(x))/15
1 Answer
- germanoLv 79 years agoFavourite answer
Hello,
∫ {(2 /x⁴) + [4 /(15x)]} dx =
let's rewrite the integral as:
∫ [2x^(- 4) + (4 /15)(1 /x)] dx =
let's split into two integrals pulling constants out:
2 ∫ x^(- 4) dx + (4 /15) ∫ (1 /x) dx =
2 [1/(- 4+1)] x^(- 4+1) + (4/15) ln | x | + C =
2 [1/(- 3)] x^(- 3) + (4/15) ln | x | + C =
- [2 /(3x³)] + (4/15) ln | x | + C
the answer is - [2 /(3x³)] + (4/15) ln | x | + C (why not?)
I hope it helps
