(1/. a)arctan(u/. a)+c =
(1/a)arctan(u/a) + c = arctan(u/a)/a + c
To simplify the expression (1/a)arctan(u/a) + c, we can start by rearranging the terms:
(1/a)arctan(u/a) + c = arctan(u/a)/a + c
Now, let’s apply the arctan addition formula, which states that arctan(x) + arctan(y) = arctan((x+y)/(1-xy)):
arctan(u/a)/a + c = arctan((u/a + 0)/(1 – u/a * 0))/a + c
Since 0 is the identity element for addition, we can simplify the expression further:
arctan(u/a)/a + c = arctan(u/a)/a + c = arctan(u/a)/a + a * c/a
Now, we can combine the two fractions:
arctan(u/a)/a + a * c/a = (arctan(u/a) + a * c)/a
Therefore, the simplified expression is:
(1/a)arctan(u/a) + c = (arctan(u/a) + a * c)/a
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