1) _{[ o]}^{[ n]} {x} dx = n/2      where {x} means fractional part of x      (n belongs to  

 

integers)

 

 

2)  _{[ o]}^{[n ]} [x] dx = n (n-1)/2   ( n belongs to integers)

 

 

3) _{[ a]}^{[ b]} [x] dx = 1/2( [b] - [a] ) ( [b] +[a] - 1) + [b]{b} - [a]{a}       ( a , b are not

 

integers)

 

 

 

4)_{[a ]}^{[b ]}  modulus (x)/x dx = modulus(b) - modulus (a)

 

 

 

5)_{[ 0]}^{[  ]} dx / (x+^{[ 2]}x² +1)^{n   =} n/n² - 1

 

 

6)_{[o ]}^{[ /2]} sinⁿx / sinⁿx + cosⁿx dx = /4

 

the above formula is valid for( tan and cot), (sec and cosec) also

 

 

7)_{[ ]}^{[ ]} e^x xⁿ dx = e^x(xⁿ-nx^n-1 + n*n-1x^n-2 -....const)

 

for example:-

 

 

e^xx³ dx =e^x(x³ - 3x² +6x - 6)