What is the integral of 7/(5x^2+11) ?

The integral of 7/(5x^2+11) is 7/(sqrt(55))arctan(sqrt(5/11)x)+C

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integral of 7/(5x^2+11)

\int \frac{7}{5 x ^{2} + 11} d x

\frac{7}{55} arctan (\frac{5}{11} x) + C

Solution steps

\int \frac{7}{5 x ^{2} + 11} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{5 x ^{2} + 11} d x

Apply Integral Substitution

= 7 \cdot \int \frac{1}{55 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 7 \cdot \frac{1}{55} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 7 \cdot \frac{1}{55} arctan (u)

Substitute back

u = \frac{5}{11} x

= 7 \cdot \frac{1}{55} arctan (\frac{5}{11} x)

Simplify

7 \cdot \frac{1}{55} arctan (\frac{5}{11} x) : \frac{7}{55} arctan (\frac{5}{11} x)

= \frac{7}{55} arctan (\frac{5}{11} x)

Add a constant to the solution

= \frac{7}{55} arctan (\frac{5}{11} x) + C

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What is the integral of 7/(5x^2+11) ?
The integral of 7/(5x^2+11) is 7/(sqrt(55))arctan(sqrt(5/11)x)+C