What is the integral of 1/(16+25x^2)+2/(3(x-2)) ?

The integral of 1/(16+25x^2)+2/(3(x-2)) is 1/20 arctan(5/4 x)+2/3 ln|x-2|+C

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integral of 1/(16+25x^2)+2/(3(x-2))

\int \frac{1}{16 + 25 x ^{2}} + \frac{2}{3 ( x - 2 )} d x

\frac{1}{20} arctan (\frac{5}{4} x) + \frac{2}{3} ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{1}{16 + 25 x ^{2}} + \frac{2}{3 ( x - 2 )} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{16 + 25 x ^{2}} d x + \int \frac{2}{3 ( x - 2 )} d x

\int \frac{1}{16 + 25 x ^{2}} d x = \frac{1}{20} arctan (\frac{5}{4} x)

\int \frac{2}{3 ( x - 2 )} d x = \frac{2}{3} ln ∣ x - 2 ∣

= \frac{1}{20} arctan (\frac{5}{4} x) + \frac{2}{3} ln ∣ x - 2 ∣

Add a constant to the solution

= \frac{1}{20} arctan (\frac{5}{4} x) + \frac{2}{3} ln ∣ x - 2 ∣ + C

x \to π lim (- 9 sin (\frac{x}{2}))

f (x) = (- 9 x^{2} + 16)^{2}

\int 6 x d x

\int \frac{x + 1}{x ^{2} - 4 x + 3} d x

y = x^{2} - 2, y = 7

What is the integral of 1/(16+25x^2)+2/(3(x-2)) ?
The integral of 1/(16+25x^2)+2/(3(x-2)) is 1/20 arctan(5/4 x)+2/3 ln|x-2|+C