Question

find the antiderivative of 4-(3/(1+x^2))

Answer 1

\[\int\limits_{}^{}(4-\frac{3}{1+x^2}) dx =\int\limits_{}^{}4 dx -3\int\limits_{}^{}\frac{1}{1+x^2} dx\]

Answer 2

\[4x-3 \cdot \tan^{-1}(x)+C\]

Answer 3

we haven't learned integrals yet though, is there an alternative way?

Answer 4

and where does the tan come from? Im lost

Answer 5

the 2nd integral you need to know the derivative of tan inverse to answer that
and the derivative of 4x is 4 so the antiderivative of 4 is 4x