ddx∫x2x3 1log⁡tdt is equal to

# $\frac{\mathrm{d}}{\mathrm{dx}}\left({\int }_{{\mathrm{x}}^{2}}^{{\mathrm{x}}^{3}} \frac{1}{\mathrm{log}\mathrm{t}}\mathrm{dt}\right)$ is equal to

1. A

$\frac{1}{\mathrm{log}\mathrm{x}}$

2. B

$\frac{{\mathrm{x}}^{2}}{\mathrm{log}\mathrm{x}}$

3. C

$\frac{{\mathrm{x}}^{2}-\mathrm{x}}{\mathrm{log}\mathrm{x}}$

4. D

None of these

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

$\begin{array}{l}\frac{\mathrm{d}}{\mathrm{dx}}\left({\int }_{{\mathrm{x}}^{2}}^{{\mathrm{x}}^{3}} \frac{1}{\mathrm{log}\mathrm{t}}\cdot \mathrm{dt}\right)=\frac{1}{\mathrm{log}{\mathrm{x}}^{3}}\cdot \frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}{\right)}^{3}-\frac{1}{\mathrm{log}{\mathrm{x}}^{2}}\cdot \frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{x}}^{2}\right)\\ =\frac{3{\mathrm{x}}^{2}}{3\mathrm{log}\mathrm{x}}-\frac{2\mathrm{x}}{2\mathrm{log}\mathrm{x}}\\ ⇒\frac{\mathrm{d}}{\mathrm{dx}}\left({\int }_{{\mathrm{x}}^{2}}^{{\mathrm{x}}^{3}} \frac{1}{\mathrm{log}\mathrm{t}}\mathrm{dt}\right)=\frac{1}{\mathrm{log}\mathrm{x}}\cdot \left({\mathrm{x}}^{2}-\mathrm{x}\right)\end{array}$