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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{2 x^2 \cos \left(x^2\right)-\sin \left(x^2\right)}{x^2} d x=\)

  1. A \(\frac{\sin \left(x^2\right)}{x^2}+c\)
  2. B \(\frac{\cos \left(x^2\right)}{x^2}+c\)
  3. C \(\sin \left(x^2\right)+\mathrm{c}\)
  4. D \(\frac{\sin \left(x^2\right)}{x}+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\sin \left(x^2\right)}{x}+c\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Let } h=\int \frac{2 x^2 \cos \left(x^2\right)-\sin \left(x^2\right)}{x^2} d x \\ = & \int \frac{x \cdot d\left(\sin \left(x^2\right)\right)-\sin \left(x^2\right) \cdot d(x)}{x^2} \\ = & \int d\left(\frac{\sin \left(x^2\right)}{x}\right)=\frac{\sin…