What is the integral of 1/(1+121x^2) ?

The integral of 1/(1+121x^2) is 1/11 arctan(11x)+C

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integral of 1/(1+121x^2)

\int \frac{1}{1 + 121 x ^{2}} d x

\frac{1}{11} arctan (11 x) + C

Solution steps

\int \frac{1}{1 + 121 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{11 ( 1 + u ^{2} )} d u

Take the constant out:

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

= \frac{1}{11} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= \frac{1}{11} arctan (u)

Substitute back

u = 11 x

= \frac{1}{11} arctan (11 x)

Add a constant to the solution

= \frac{1}{11} arctan (11 x) + C

7 x e^{6 x}

\frac{d}{d t} (7 t^{2} - 5 t + 3)

x^{\frac{1}{2}}

\frac{\partial}{\partial x} (- 2 x e^{2 x y})

x \to 1 lim (101)

What is the integral of 1/(1+121x^2) ?
The integral of 1/(1+121x^2) is 1/11 arctan(11x)+C