Kc Sinha Mathematics Class 12 Solutions Pdf Fixed May 2026

It is a legendary book for mastering calculus, algebra, and vectors. However, there is a massive problem students face online:

Integrate ∫ x sin⁻¹ x dx

If you are a Class 12 student preparing for your Board Exams (especially CBSE, Bihar Board, or UP Board), you have almost certainly heard of—or struggled with— book. Kc Sinha Mathematics Class 12 Solutions Pdf Fixed

Let I = ∫ x sin⁻¹ x dx Put sin⁻¹ x = t → x = sin t, dx = cos t dt I = ∫ sin t . t . cos t dt = (1/2) ∫ t sin 2t dt Apply integration by parts: = (1/2)[ t (-cos 2t)/2 - ∫ (-cos 2t)/2 dt ] = - (t cos 2t)/4 + (1/8) sin 2t + C Back substitute: t = sin⁻¹ x, sin 2t = 2x√(1-x²), cos 2t = 1-2x² Final answer: (1/4)(2x²-1) sin⁻¹ x + (x/4)√(1-x²) + C Crystal clear, no missing steps. Yes – for solving doubts. No – for concept building. It is a legendary book for mastering calculus,