Question
\(\int \frac{1+3x}{(1-x)(3x-5)}=\)
A 2 ln |1 − x| − 3 ln |3x − 5| + C
B 2 ln |1 − x| − 27 ln |3x − 5| + C
C −2 ln |1 − x| − 3 ln |3x − 5| + C
D −2 ln |1 − x| − 9 ln |3x − 5| + C
Answer/Explanation
Question
\(\int_{2}^{3}\frac{3}{(x-1)(x+2)} dx=\)
(A)\(-\frac{33}{20}\) (B)\(-\frac{9}{20}\) (C)\(ln\left ( \frac{5}{2} \right )\) (D)\(ln\left ( \frac{5}{2} \right )\) (E)\(ln\left ( \frac{2}{5} \right )\)
Answer/Explanation
Question
\(\int \frac{dx}{(x-1)(x+3)}=\)
(A)\(\frac{1}{4}ln\left | \frac{x-1}{x+3} \right |+C\)
(B)\(\frac{1}{4}ln\left | \frac{x+3}{x-1} \right |+C\)
(C)\(\frac{1}{2}ln\left | (x-1)(x+3) \right |+C\)
(D)\(\frac{1}{2}ln\left | \frac{2x+2}{(x-1)(x+3)} \right |+C\)
(E)\(ln\left | (x-1)(x+3) \right |+C\)
Answer/Explanation
Ans:A
Question
\(\frac{dx}{(x-1)(x+2)}\)
(A) \(\frac{1}{3}ln|\frac{x-1}{x+2}|+c\)
(B) \(\frac{1}{3}ln|\frac{x+2}{x-1}|+c\)
(C) \(\frac{1}{3}ln|(x+2)(x-1)|+c\)
(D) \((ln|x-1|)(ln|x+2|)+c\)
(E) \(ln|(x+2)^2(x-1)|+c\)
Answer/Explanation
Ans:A
