CBSE Class 12-science Maths Integrals

• Ans is 1/2 but I need the stepwise solution
  
• `I=int x cos^(-1)xdx`
• Pl ans as fast as possible 
  
• Integrate.    x arcsinx dx
• Integration ( sin^-1 (x)^1/2 – cos^-1 (x)^1/2/sin^-1 (x)^1/2 + cos^-1 (x)^1/2) dx
•   Integration ( sin^-1 (x)^1/2 – cos^-1 (x)^1/2/sin^-1 (x)^1/2 + cos^-1 (x)^1/2) dx
• Integration 2 x³ e^{x square} dx explain in great detail and give full solution 
• Integration x . log(x + 1)  dx explain in great detail and give full solution
• Integration  x² cos³ x dx  explain in great detail and give full solution
• Integrate:

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