What is the integral of 3/(1+x^2) ?

The integral of 3/(1+x^2) is 3arctan(x)+C

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integral of 3/(1+x^2)

\int \frac{3}{1 + x ^{2}} d x

3 arctan (x) + C

Solution steps

\int \frac{3}{1 + x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= 3 arctan (x)

Add a constant to the solution

= 3 arctan (x) + C

y^{^{''}} + y = 4 x sin (x)

x \to + 3 lim ((\frac{x - 1}{2 x - 4})^{\frac{1}{x - 3}})

y^{^{''}} = - 4 \cdot y

\int \frac{1}{16 e ^{- 3 x} + e ^{3 x}} d x

y = x e^{x}