Integration part 1

Integrate: 1/x^2-a^2 dx. Integrate: 1/a^2-x^2 dx . Integration of : 1/x^2-a^2 dx. Integration of : 1/a^2-x^2 dx . Integration most important questions.

Integral of the form int[xf\'(x)+f(x)]dx can be evaluated by using integration by parts in first integral and leaving second integral as it is.Now answer the question: int[1/(x^4+1)-(4x^4)/(x^4+1)^2]dx= (A) x^2/(x^4+1)+c (B) x^3/(x^4+1)+c (C) x/(x^4+1)+c (D) none of these

Statement 1: int(dx)/(x^3sqrt(1+x^4))=-1/2sqrt(1+1/(x^4))+C Statement 2: For integration by parts, we have to follow ILATE rule. Which of the following Statements is/are correct ?

Integral of the form int[xf\'(x)+f(x)]dx can be evaluated by using integration by parts in first integral and leaving second integral as it is.Now answer the question: int[x^(x+1)(logx+1)+x^x]dx= (A) x^(x+2)+c (B) x^(x+1)+c (C) x^x+x+c (D) none of these

Integral part of (sqrt2+1)^6 is

Let f(x)=(1)/(pi) (sin^(-1)x+cos^(-1)x+tan^(-1)x)+((x+1))/(x^(2)+2x+10) , if the absolute maximum value of f(x)=M , then the integral part of (1)/(M) is _____________ .

The area enclosed by the circle x^2+(y+2)^2=16 is divided into two parts by the x-axis. Find by integration, the area of the smaller part.