What is the integral of 3/(144+49x^2) ?

The integral of 3/(144+49x^2) is 1/28 arctan(7/12 x)+C

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integral of 3/(144+49x^2)

\int \frac{3}{144 + 49 x ^{2}} d x

\frac{1}{28} arctan (\frac{7}{12} x) + C

Solution steps

\int \frac{3}{144 + 49 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}{144 + 49 x ^{2}} d x

Apply Integral Substitution

= 3 \cdot \int \frac{1}{84 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 3 \cdot \frac{1}{84} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 3 \cdot \frac{1}{84} arctan (u)

Substitute back

u = \frac{7}{12} x

= 3 \cdot \frac{1}{84} arctan (\frac{7}{12} x)

Simplify

3 \cdot \frac{1}{84} arctan (\frac{7}{12} x) : \frac{1}{28} arctan (\frac{7}{12} x)

= \frac{1}{28} arctan (\frac{7}{12} x)

Add a constant to the solution

= \frac{1}{28} arctan (\frac{7}{12} x) + C

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What is the integral of 3/(144+49x^2) ?
The integral of 3/(144+49x^2) is 1/28 arctan(7/12 x)+C