4/2x+1 we express this function as 4/2 X(multiply) 1 /x+1 then it should be 2ln (x+1)
then in solutions why there is (2x+1)???
its not 4/2 multiply 1/x+1. anyway its better off thinking about chain rule the other way round, find the derivative of the bottom function and do 1/derivative multiplied by standard integral. here that is derivative of 2x+1 which is 2 divided by 4 multiplied by the standard integral of 1/f(x) which is lnf(x)
The solution that i got in which they expand the bracket by using formula a^2 +2ab+b^2 and then integrate each term separately.But why i cant do like that
The solution that i got in which they expand the bracket by using formula a^2 +2ab+b^2 and then integrate each term separately.But why i cant do like that
(e^x +1)^3 /3??
If it were (x+1)2, you could integrate it to get (x+1)3/3 (as the derivative of x+1 is 1), but since it is (ex+1)2, that method is invalid, and expanding the brackets is the best way to do this.
If it were (x+1)2, you could integrate it to get (x+1)3/3 (as the derivative of x+1 is 1), but since it is (ex+1)2, that method is invalid, and expanding the brackets is the best way to do this.
I actually got the right answer in this question but i am thinking that if we replace 1 + tan^2x with sec^2x it gives a different answer(-cotx . tanx +c) ? so how I know that in which form i have to give answer unless they not stated in question
I actually got the right answer in this question but i am thinking that if we replace 1 + tan^2x with sec^2x it gives a different answer(-cotx . tanx +c) ? so how I know that in which form i have to give answer unless they not stated in question
you should get equivalent answers. the examiners are experts as this & will know if you done good.
I actually got the right answer in this question but i am thinking that if we replace 1 + tan^2x with sec^2x it gives a different answer(-cotx . tanx +c) ? so how I know that in which form i have to give answer unless they not stated in question