What is the integral of 1/(x^2+10x+26) ?

The integral of 1/(x^2+10x+26) is arctan(x+5)+C

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integral of 1/(x^2+10x+26)

\int \frac{1}{x ^{2} + 10 x + 26} d x

arctan (x + 5) + C

Solution steps

\int \frac{1}{x ^{2} + 10 x + 26} d x

Complete the square

x^{2} + 10 x + 26 : (x + 5)^{2} + 1

= \int \frac{1}{( x + 5 ) ^{2} + 1} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 1} d u

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

Use the common integral:

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

= arctan (u)

Substitute back

u = x + 5

= arctan (x + 5)

Add a constant to the solution

= arctan (x + 5) + C

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What is the integral of 1/(x^2+10x+26) ?
The integral of 1/(x^2+10x+26) is arctan(x+5)+C