# Integration by Parts

First of all, why Integration by Parts?As we know that But what's the integration of So, we use integration by parts technique for the integration of product of functions (

*x*and cos

*x*in product form ).

# Formula for Integration by Parts

Suppose two functions*u*and

*v*are in product form, then formula for finding their integration is We can also remember the short formula for Integration by Parts which is usually without

*dx*

# Practice Problems

EvaluateExample 1. |

*Solution*Here,

*u*=

*x*

_{}

*u*

^{'}= 1

v = cosx _{} |

*Answer* EvaluateExample 2. |

*Solution*Here,

*u*= 2

*x*

^{2}

_{}

*u*

^{'}= 4

*x*

v = sinx _{} |

The later is again product of functions, and we have to use Integration by parts again. In the example above we have already found that, so using result from the above, we have

*Answer*NOTE: 4

*c*and

*c*both are constants, so ignore 4.

Integration by Parts of ln Functions

Integration by Parts of Exponential Functions