Basic Integration Formulas

• ( int 0 , dx = C )
• ( int 1 , dx = x + C )
• ( int x^n , dx = frac{x^{n+1}}{n+1} + C ), where ( n neq -1 )
• ( int frac{1}{x} , dx = ln|x| + C )

Trigonometric Functions

• ( int sin x , dx = -cos x + C )
• ( int cos x , dx = sin x + C )
• ( int sec^2 x , dx = tan x + C )
• ( int csc^2 x , dx = -cot x + C )
• ( int sec x tan x , dx = sec x + C )
• ( int csc x cot x , dx = -csc x + C )

Inverse Trigonometric Functions

• ( int frac{1}{sqrt{1-x^2}} , dx = sin^{-1} x + C )
• ( int frac{-1}{sqrt{1-x^2}} , dx = cos^{-1} x + C )
• ( int frac{1}{1+x^2} , dx = tan^{-1} x + C )

Exponential Functions

• ( int e^x , dx = e^x + C )
• ( int a^x , dx = frac{a^x}{ln a} + C ), where ( a > 0 ) and ( a neq 1 )

Logarithmic Functions

• ( int ln x , dx = x ln x – x + C )
• ( int log_a x , dx = frac{x log_a x – x}{ln a} + C ), where ( a > 0 ) and ( a neq 1 )