TS EAMCET · Maths · Indefinite Integration
\(\begin{aligned} & \text { If } 5(f(x))^2=x f(x)+30 \text { and } \ & \int \frac{\left(3 x^3+\left(1-30 x^2\right) f(x)\right)}{(10 f(x)-x)\left(x^3-f(x)\right)^2} d x \ & =\frac{A}{B x^3+D f(x)}+C \text { then } A+B+D=\end{aligned}\)
- A 2
- B 1
- C \(\frac{1}{2}\)
- D -1
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & 5(f(x))^2=x f(x)+30 \Rightarrow 10 f(x) f^{\prime}(x)=x f^{\prime}(x)+f(x) \\ & \Rightarrow \quad(10 f(x)-x) f^{\prime}(x)=f(x) \end{aligned}\) Now,…
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