What is the integral of 6/((1+t^2)) ?

The integral of 6/((1+t^2)) is 6arctan(t)+C

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integral of 6/((1+t^2))

integral

\frac{6}{( 1 + t ^{2} )}

6 arctan (t) + C

Solution steps

\int \frac{6}{1 + t ^{2}} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int \frac{1}{1 + t ^{2}} d t

Use the common integral:

\int \frac{1}{1 + t ^{2}} d t = arctan (t)

= 6 arctan (t)

Add a constant to the solution

= 6 arctan (t) + C

What is the integral of 6/((1+t^2)) ?
The integral of 6/((1+t^2)) is 6arctan(t)+C