Friday, May 4, 2012

`int (x + 4)6^((x+4)^2) dx` Find the indefinite integral

`int(x+4)6^((x+4)^2)dx=`


We will make substitution `u=(x+4)^2.` Differentiation the substitution gives us `du=2(x+4)dx.`


Now we rewrite the integral.


`1/2 int 6^((x+4)^2)2(x+4)dx=`


The above integral is equal to the starting one because `1/2` and `2` cancel out. Now we use the substitution while.


`1/2int6^udu=1/2cdot6^u/ln 6+C` 


To write the final solution we simply return the substitution i.e. we put `(x+4)^2` instead of `u.`


`6^((x+4)^2)/(2ln6)+C` where C is a constant                                                                                  

No comments:

Post a Comment

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Thomas Jefferson’s election in 1800 can be called the “Revolution of 1800” because it was the first time in America’s short history that pow...