What is the integral of (144)/(36+x^2) ?

The integral of (144)/(36+x^2) is 24arctan(x/6)+C

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integral of (144)/(36+x^2)

\int \frac{144}{36 + x ^{2}} d x

24 arctan (\frac{x}{6}) + C

Solution steps

\int \frac{144}{36 + x ^{2}} d x

Take the constant out:

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

= 144 \cdot \int \frac{1}{36 + x ^{2}} d x

Apply Integral Substitution

= 144 \cdot \int \frac{1}{6 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 144 \cdot \frac{1}{6} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 144 \cdot \frac{1}{6} arctan (u)

Substitute back

u = \frac{x}{6}

= 144 \cdot \frac{1}{6} arctan (\frac{x}{6})

Simplify

144 \cdot \frac{1}{6} arctan (\frac{x}{6}) : 24 arctan (\frac{x}{6})

= 24 arctan (\frac{x}{6})

Add a constant to the solution

= 24 arctan (\frac{x}{6}) + C

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What is the integral of (144)/(36+x^2) ?
The integral of (144)/(36+x^2) is 24arctan(x/6)+C