What is the integral of (100)/(25x^2+36) ?

The integral of (100)/(25x^2+36) is 10/3 arctan(5/6 x)+C

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integral of (100)/(25x^2+36)

\int \frac{100}{25 x ^{2} + 36} d x

\frac{10}{3} arctan (\frac{5}{6} x) + C

Solution steps

\int \frac{100}{25 x ^{2} + 36} d x

Take the constant out:

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

= 100 \cdot \int \frac{1}{25 x ^{2} + 36} d x

Apply Integral Substitution

= 100 \cdot \int \frac{1}{30 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 100 \cdot \frac{1}{30} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 100 \cdot \frac{1}{30} arctan (u)

Substitute back

u = \frac{5}{6} x

= 100 \cdot \frac{1}{30} arctan (\frac{5}{6} x)

Simplify

100 \cdot \frac{1}{30} arctan (\frac{5}{6} x) : \frac{10}{3} arctan (\frac{5}{6} x)

= \frac{10}{3} arctan (\frac{5}{6} x)

Add a constant to the solution

= \frac{10}{3} arctan (\frac{5}{6} x) + C

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What is the integral of (100)/(25x^2+36) ?
The integral of (100)/(25x^2+36) is 10/3 arctan(5/6 x)+C