00:01
One question we are asked to find the indefinite integral for this given and also we are asked to check it with using differentiation.
00:08
Now let us first try to find the indefinite integral that is integral x plus 3 dx.
00:16
Since it is some we can split it into two parts that is integral x dx plus integral 3dx.
00:28
Here in on the right i am writing some formulas used for dx.
00:31
Integration formulas i think you are familiar with this that is integral x power n dx equal to x4 n plus 1 by n plus 1 and the second one is integral some constant c dx equal to c x x so these are two basic formulas now here in this you can see that here x is nothing but we have power 1 so this we can write x power 1 plus 1 divided by 1 plus 1 from the first formula.
01:10
Plus 3 is a constant.
01:12
So integral 3dx would become 3 times x plus k.
01:17
Since it's a different integration, we should add a constant at the last.
01:22
So it becomes x squared by 2 plus 3x plus k.
01:27
So this is the final answer for integration.
01:30
Now to check this answer we have to differentiate the answer by differentiating we should get the function value that is x plus 3.
01:39
Now let us check it.
01:41
Second, let us derive to d by dx of x squared by 2 plus 3x plus k...