Question
Download Solution PDF\(\rm \int {5x\over x^2+3x-4}dx\) =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Integral property:
- ∫ xn dx = \(\rm x^{n+1}\over n+1\)+ C ; n ≠ -1
- \(\rm∫ {1\over x} dx = \ln x\) + C
- ∫ ex dx = ex+ C
- ∫ ax dx = (ax/ln a) + C ; a > 0, a ≠ 1
- ∫ sin x dx = - cos x + C
- ∫ cos x dx = sin x + C
Calculation:
I = \(\rm \int {5x\over x^2+3x-4}dx\)
I = \(\rm \int {5x\over (x-1)(x+4)}dx\)
I = \(\rm \int {(x+4)+(4x-4)\over (x-1)(x+4)}dx\)
I = \(\rm \int{1\over x-1}dx+\int{4\over x+4} dx\)
I = ln (x - 1) + 4 ln (x + 4) + c
Last updated on Jun 18, 2025
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