The equation of the tangent to the curvey=∫xx2 log⁡tdt  at x=2 is

y=∫xx2 log⁡tdt=(tlog⁡t−t)xx2=2x2−xlog⁡x−x2+x⇒y(2)=6log⁡2−2Also, y′(2)=7log⁡2Thus, equation of tangent at x = 2 isy−(6log⁡2−2)=(7log⁡2)(x−2) or y+8log⁡2+2=(7log⁡2)(x)