FTC #1- G ( x ) = f ′ ( x ) {\displaystyle G(x)=f^{\prime }(x)} or in other words d d x [ ∫ a ( x ) b ( x ) F ( x ) d x ] {\displaystyle {\frac {d}{dx}}\left[\int \limits _{a(x)}^{b(x)}F(x)dx\right]} is b ′ ( x ) ∗ f ( b ( x ) ) − a ′ ( x ) ∗ f ( a ( x ) ) {\displaystyle \ b^{\prime }(x)*f(b(x))-a^{\prime }(x)*f(a(x))}
17) y = ∫ 1 − 3 x 1 u 3 ( 1 + u 2 ) d u {\displaystyle y=\int \limits _{1-3x}^{1}{\frac {u^{3}}{(1+u^{2})}}du}
so using the formula we get y= ( 0 ) ∗ f ( 1 ) − ( − 3 ) ∗ f ( 1 − 3 x ) {\displaystyle (0)*f(1)-(-3)*f(1-3x)}
which is equal to ( 3 ) ∗ f ( 1 − 3 x ) {\displaystyle (3)*f(1-3x)}
which is= 3 ∗ ( 1 − 3 x ) 3 ( 1 + ( 1 − 3 x ) 2 ) {\displaystyle 3*{\frac {(1-3x)^{3}}{(1+(1-3x)^{2})}}}
or simplified to 3 ∗ ( 1 − 3 x ) 3 ( 1 + ( 1 − 3 x ) 2 ) {\displaystyle {\frac {3*(1-3x)^{3}}{(1+(1-3x)^{2})}}}
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or in other words ![{\displaystyle {\frac {d}{dx}}\left[\int \limits _{a(x)}^{b(x)}F(x)dx\right]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9331129b1175ef32e6c2e77b2e98e903c62fa668)
is 
