∫(x2 dx/(a+bx)2) equals

Question

∫(x2 dx/(a+bx)2) equals (A) (1/b2) [ x + (2a/b) log |(a+bx)| - (a2/b) (1/(a+bx))] +c (B) (1/b2) [ x - (2a/b) log |(a+bx)| + (a2/b) (1/(a+bx))] +c (C) (1/b2) [ x +(a/b)- (2a/b) log |(a+bx)| - (a2/b) (1/(a+bx))] +c (D) (1/b2) [ x +(a/b) + (2a/b) log |(a+bx)| + (a2/b) (1/(a+bx))] +c

Tardigrade Admin · Accepted Answer

Correct answer is (c) (1/b2) [ x +(a/b)- (2a/b) log |(a+bx)| - (a2/b) (1/(a+bx))] +c

Q. $\int \frac{x ^{2} d x}{( a + b x ) ^{2}}$ equals

$\frac{1}{b ^{2}} [x + \frac{2 a}{b} l o g ∣ (a + b x) ∣ - \frac{a ^{2}}{b} \frac{1}{( a + b x )}] + c$

$\frac{1}{b ^{2}} [x - \frac{2 a}{b} l o g ∣ (a + b x) ∣ + \frac{a ^{2}}{b} \frac{1}{( a + b x )}] + c$

$\frac{1}{b ^{2}} [x + \frac{a}{b} - \frac{2 a}{b} l o g ∣ (a + b x) ∣ - \frac{a ^{2}}{b} \frac{1}{( a + b x )}] + c$

$\frac{1}{b ^{2}} [x + \frac{a}{b} + \frac{2 a}{b} l o g ∣ (a + b x) ∣ + \frac{a ^{2}}{b} \frac{1}{( a + b x )}] + c$

Correct answer is (c) $\frac{1}{b ^{2}} [x + \frac{a}{b} - \frac{2 a}{b} l o g ∣ (a + b x) ∣ - \frac{a ^{2}}{b} \frac{1}{( a + b x )}] + c$

Q. ∫(a+bx)2x2dx​ equals

b21​[x+b2a​log∣(a+bx)∣−ba2​(a+bx)1​]+c

b21​[x−b2a​log∣(a+bx)∣+ba2​(a+bx)1​]+c

b21​[x+ba​−b2a​log∣(a+bx)∣−ba2​(a+bx)1​]+c

b21​[x+ba​+b2a​log∣(a+bx)∣+ba2​(a+bx)1​]+c