Question

Assertion :$\int \frac{3x+7}{3x^2+14x-5}dx=\frac{1}{2}\log |3x^2+14x-5|+c$

Reason :$\int \frac{f^{\prime }\left(x\right)}{f\left(x\right)}dx=\log |f\left(x\right)|+c$

• A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
• B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion and Reason are true and Reason is the correct explanation of Assertion

$A=\int \frac{3x+7}{3x^2+14x-5}dx=\frac{1}{2}\int \frac{6x+14}{3x^2+14x-5}dx$

$=\frac{1}{2}\log \mid 3x^2+14x-5\mid +c$ ..... $(\because \int \frac{f^{\prime }\left(x\right)}{f\left(x\right)}dx=\log |f\left(x\right)|+c)$
R is true
Hence, A and R are true and R is the correct explanation of A.