Antiderivatives of radical function and explain the solution

BenoguigoliB

BenoguigoliB

Answered question

2021-09-10

Antiderivatives of radical function and explain the solution
(3x+7)dx

Answer & Explanation

Caren

Caren

Skilled2021-09-11Added 96 answers

We need to find (3x+7) dx 
In order to find the integral, we will now use the formula shown below:
xn dx =xn+1n+1+c
Now, xn dx =xn+1n+1+c, here c is the constant of integration and n is any real number.
Now, x=x12
Thus,
x12 dx =x12+112+1+c
=x1+221+22+c
=x3232+c
=23x32+c
Hence, x12 dx =23x32+c
And
1=x0
Hence,
1 dx =x0 dx 
=x0+10+1+c
=x+c
Thus, 1 dx =x+c
We now had to assess (3x+7) dx 
Using [af(x)+bg(x)] dx =af(x) dx +bg(x) dx 
(3x+7) dx =(3x+7x0) dx 
=3x dx +7x0 dx 
=3(23x32)+7x+C
 

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