If ∫ (1/6 x2+13 x+6) d x=(1/a) ln |(b x+2/2 x+b)|+C, where a, b ∈ R and C is constant of integration to is equal to

Question

If ∫ (1/6 x2+13 x+6) d x=(1/a) ln |(b x+2/2 x+b)|+C, where a, b ∈ R and C is constant of integration to is equal to (A) 3 (B) 5 (C) 7 (D) 8

Tardigrade Admin · Accepted Answer

Given integral =∫ (1/(2 x+3)(3 x+2)) d x=∫(((-2/5)/(2 x+3))+((3/5)/(3 x+2))) d x I=(-1/5) ln (2 x+3)+(1/5) ln (3 x+2)+C =(1/5) ln |(3 x +2/2 x +3)|+ C ∴ a =5 text and b =3 ⇒ a + b =8

Q. If ∫6x2+13x+61​dx=a1​ln∣∣​2x+bbx+2​∣∣​+C, where a,b∈R and C is constant of integration to is equal to

3

5

7

8

Given integral =∫(2x+3)(3x+2)1​dx=∫((2x+3)5−2​​+(3x+2)53​​)dx I=5−1​ln(2x+3)+51​ln(3x+2)+C =51​ln∣∣​2x+33x+2​∣∣​+C ∴a=5 and b=3⇒a+b=8

Q. If $\int \frac{1}{6 x ^{2} + 13 x + 6} d x = \frac{1}{a} ln ∣ ∣ \frac{b x + 2}{2 x + b} ∣ ∣ + C$ , where $a, b \in R$ and $C$ is constant of integration to is equal to