a) ( int frac{operatorname{arctg} x}{1+x^{2}} d x )

Question

Accepted Answer

Step:1 ：Let ( y = operatorname{arctg} x )Step:2 ：Differentiate with respect to x: (frac{d y}{d x}=frac{1}{1+x^2} )Step:3 ：Substitute y back into the integral: (int y d y = frac{1}{2}y^2 + C )Step:4 ：Substitute ( operatorname{arctg} x ) back as y: ( frac{1}{2}ln(1+x^2) + C )

Answer

Step: 1 ：Let ( y = operatorname{arctg} x )Step: 2 ：Differentiate with respect to x: (frac{d y}{d x}=frac{1}{1+x^2} )Step: 3 ：Substitute y back into the integral: (int y d y = frac{1}{2}y^2 + C )Step: 4 ：Substitute ( operatorname{arctg} x ) back as y: ( frac{1}{2}ln(1+x^2) + C )

a) \( \int \frac{\operatorname{arctg} x}{1+x^{2}} d x \)

Answer

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