Ways to attack an integral

Ways to attack an integral

1. Basic integral

   • Formula
     • X^n+1/n+1
   • Integration Common Functions Function Integral Multiplication by constant ∫cf(x) dx c∫f(x) dx Power Rule (n≠-1) ∫xn dx xn+1/(n+1) + C Sum Rule ∫(f + g) dx ∫f dx + ∫g dx Difference Rule ∫(f - g) dx ∫f dx - ∫g dx

2. Integration by parts

   • The integration by parts is either cyclic and by using formula
     • By formula
       • You use the formula to solve the problem by arraniging the values according to LIPET
         • LIPET
           • "The word “LIPET” is an acronym, meaning that each letter stands for a word. In this case, the letters represent different types of functions. These identifications are: L = Logarithmic function I = Inverse trigonometric function P = Polynomial function E = Exponential function T = Trigonometric function:
         • How to identify it
           • These are identified by looking for a ln in the integration
     • cycle
       • This is used when you there is an ln in the equation as these is only useful when you have a trigonometrical and exponential integral

3. Substitution

   • change of variables
     • The change of variables is identified by a complex looking substitution with u integral, solve it as if solving with sobustitution with u but the remaining parts just arrange it with the reciplocal form in te equation
     • Example
   • Simpe substitution with u
     • Example
     • This is solved by taking a value from the equation, derivating it and putting it in the equation canceling a value and putting down u

4. trigonometric integrals

   • Sin and cosine
     • Same as the substution with the only exception that you use the derivate of sine and cosine to solve, integrate according to the integrals table
   • Tan and Sec
     • Integrate by using trigonometrical identities, solve by obtaining sine and cosine and use simple substitution, same as sine and coninse use the table for the final integration
   • trigonometric integrals

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