indefinite integral
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Let y=x²+1, then dy=2xdx, so xdx=dy/2.

The integrand simplifies:



Cancel common factor sin(y):


Multiply by (1-cos(y))/(1-cos(y)):





Derivative of cot(y) is -csc²(y).

Derivative of csc(y) is -cot(y)csc(y).





-cot(y)+csc(y)-y/2+c, where c is the constant of integration.

Replacing y with x²+1:

-cot(x²+1)+csc(x²+1)-(x²+1)/2+c or -cot(x²+1)+csc(x²+1)-x²+C (combining constants).

by Top Rated User (804k points)

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