Question

how to integrate 1/x?

Answer 1

Answer:

∫ dx / x = logx + C

Step-by-step explanation:

To find -----> ∫ dx / x

Solution-----> We know that intregation and differentiation are reverse process , if

d / dx { f ( x ) } = F¹ ( x )

then ,

∫ F¹ ( x ) dx = f ( x ) + C

Where C , is constant of intregation .

Now , we have to find intregation of ( 1 / x ) , so first we have to find whose differentiation is 1 / x , and we know that ,

d / dx ( logx ) = 1 / x

So, ∫ 1 / x dx = logx + C

Where C is constant of integration

Additional information----->

1) ∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C

2) ∫ eˣ dx = eˣ + C

3) ∫ aˣ dx = aˣ / loga + C

4) ∫ Sinx dx = - Cosx + C

5) ∫ Cosx dx = Sinx + C

6) ∫ Cosec²x = - Cotx + C

7) ∫ Cosecx Cotx dx = - Cosecx + C

8) ∫ Sec²x dx = tanx + C

9) ∫ Secx tanx dx = Secx + C