Grade 12Integral Calculus
∑tan-1(1/(x2+x+1))
∑tan-1(1/(x2+x+1))
1 Answer
Yash Jain
The question is
∫ tan-1[ 1/(x2+x+1) ] dx
This can be written as
∫ tan-1[ {(x+1)-x} / {1+x(x+1)} ] dx
From the formula of tan-1[ (m-n) / 1+mn ], We get
∫ tan-1(x+1) – tan-1x dx
I guess now you can proceed on your own.
∫ tan-1[ 1/(x2+x+1) ] dx
This can be written as
∫ tan-1[ {(x+1)-x} / {1+x(x+1)} ] dx
From the formula of tan-1[ (m-n) / 1+mn ], We get
∫ tan-1(x+1) – tan-1x dx
I guess now you can proceed on your own.
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