# Math Help - solve a integral without using without using trigo-substitution?

1. ## solve a integral without using without using trigo-substitution?

solve a integral without using without using trigo-substitution?

2. Sure! Look it up in a table.

Really, my first question would be, "Why?"

3. Both of those are in arctangent form.
Look at the derivative of the arctangent(x).

4. I think it's an useless question, 'cause it's an immediate integral.

But you can say $y=\arctan x\implies\tan y=x\,\therefore\,y'(1+x^2)=1.$

So, $y'=\frac1{1+x^2}.$

Now integrate both sides $y+k=\int\frac1{1+x^2}\,dx.$

Since $y=\arctan x,$ we happily get that $\arctan x+k=\int\frac1{1+x^2}\,dx.$