int frac{2 x^2 cos left(x^2right)-sin left(x^ | vedclass

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(D) We are given the integral $I = \int \frac{2 x^2 \cos \left(x^2\right)-\sin \left(x^2\right)}{x^2} d x$. We can rewrite the integrand by splitting

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) We are given the integral $I = \int \frac{2 x^2 \cos \left(x^2\right)-\sin \left(x^2\right)}{x^2} d x$. We can rewrite the integrand by splitting the fraction: $I = \int \left( 2 \cos(x^2) - \frac{\sin(x^2)}{x^2} \right) dx$. Alternatively,observe the derivative of the quotient $\frac{\sin(x^2)}{x}$: $\frac{d}{dx} \left( \frac{\sin(x^2)}{x} \right) = \frac{x \cdot \frac{d}{dx}(\sin(x^2)) - \sin(x^2) \cdot \frac{d}{dx}(x)}{x^2}$ $= \frac{x \cdot (\cos(x^2) \cdot 2x) - \sin(x^2) \cdot 1}{x^2}$ $= \frac{2x^2 \cos(x^2) - \sin(x^2)}{x^2}$. Therefore,$\int \frac{2 x^2 \cos \left(x^2\right)-\sin \left(x^2\right)}{x^2} d x = \frac{\sin \left(x^2\right)}{x} + c$.

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

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