What is the integral of (21)/(4+25x^2) ?

The integral of (21)/(4+25x^2) is 21/10 arctan(5/2 x)+C

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integral of (21)/(4+25x^2)

\int \frac{21}{4 + 25 x ^{2}} d x

\frac{21}{10} arctan (\frac{5}{2} x) + C

Solution steps

\int \frac{21}{4 + 25 x ^{2}} d x

Take the constant out:

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

= 21 \cdot \int \frac{1}{4 + 25 x ^{2}} d x

Apply Integral Substitution

= 21 \cdot \int \frac{1}{10 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 21 \cdot \frac{1}{10} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 21 \cdot \frac{1}{10} arctan (u)

Substitute back

u = \frac{5}{2} x

= 21 \cdot \frac{1}{10} arctan (\frac{5}{2} x)

Simplify

21 \cdot \frac{1}{10} arctan (\frac{5}{2} x) : \frac{21}{10} arctan (\frac{5}{2} x)

= \frac{21}{10} arctan (\frac{5}{2} x)

Add a constant to the solution

= \frac{21}{10} arctan (\frac{5}{2} x) + C

n \to \infty lim (e^{n})

in v erse l a pl a ce \frac{s + 5}{( s + 1 ) ( s + 3 )}

\frac{d}{d x} (\frac{12}{x})

\int_{0}^{4} \frac{1}{x ^{2} - 16} d x

x \to 4 lim (\frac{5 - x}{x - 4})

What is the integral of (21)/(4+25x^2) ?
The integral of (21)/(4+25x^2) is 21/10 arctan(5/2 x)+C