Integration — Question 50
Original QCE Vault practice · 4 marks
Q50 · Practice questionComplex familiar4 marks
QUESTION 50 (4 marks)
Use partial fractions to evaluate ∫(x+1)(x+3)4x+7dx. WORKED SOLUTION
Practice marking scheme
4 marksANSWER23ln∣x+1∣+25ln∣x+3∣+c. Worked solution
Write (x+1)(x+3)4x+7=x+1A+x+3B. Equating numerators gives 4x+7=A(x+3)+B(x+1). Thus A+B=4 and 3A+B=7, yielding A=3/2, B=5/2. Integrate each term: ∫(x+1)(x+3)4x+7dx=23ln∣x+1∣+25ln∣x+3∣+c. Sets up partial fractions.
Determines both coefficients.
Includes the constant and correct final form.
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