What is the integral of 5/(1+x^2) ?

The integral of 5/(1+x^2) is 5arctan(x)+C

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integral of 5/(1+x^2)

\int \frac{5}{1 + x ^{2}} d x

5 arctan (x) + C

Solution steps

\int \frac{5}{1 + x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= 5 arctan (x)

Add a constant to the solution

= 5 arctan (x) + C

\frac{d}{d x} (\frac{x}{8 + x})

n = 0 \sum \infty 10 (\frac{x}{3})^{n}

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

\int \frac{( 5 x + 4 )}{5 x - 1} d x

\frac{d}{d x} (\frac{5}{( x ^{2} - 3 x ) ^{2}})