int 2 xleft(x^{2}+2right)^{-4} d x=square

Question

Accepted Answer

Step:1 ：Let ( u = x^2 + 2 ). Then, ( du = 2x dx ).Step:2 ：Rewrite the integral in terms of ( u ): ( int 2 xleft(x^{2}+2right)^{-4} d x = int u^{-4} du )Step:3 ：Integrate ( u^{-4} ) with respect to ( u ): ( int u^{-4} du = int u^{-4 + 1} frac{1}{-4 + 1} du = frac{1}{-3} u^{-3} )Step:4 ：Substitute back ( u = x^2 + 2 ): ( frac{1}{-3} u^{-3} = frac{1}{-3} (x^2 + 2)^{-3} )Step:5 ：(boxed{int 2 xleft(x^{2}+2right)^{-4} d x = frac{1}{-3} (x^2 + 2)^{-3} + C})

Answer

Step: 1 ：Let ( u = x^2 + 2 ). Then, ( du = 2x dx ).Step: 2 ：Rewrite the integral in terms of ( u ): ( int 2 xleft(x^{2}+2right)^{-4} d x = int u^{-4} du )Step: 3 ：Integrate ( u^{-4} ) with respect to ( u ): ( int u^{-4} du = int u^{-4 + 1} frac{1}{-4 + 1} du = frac{1}{-3} u^{-3} )Step: 4 ：Substitute back ( u = x^2 + 2 ): ( frac{1}{-3} u^{-3} = frac{1}{-3} (x^2 + 2)^{-3} )Step: 5 ：(boxed{int 2 xleft(x^{2}+2right)^{-4} d x = frac{1}{-3} (x^2 + 2)^{-3} + C})

$\int 2 x\left(x^{2}+2\right)^{-4} d x=\square$

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