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Popular >

integral of 1/(9x^2+1)

Solution

\int \frac{1}{9 x ^{2} + 1} d x

Solution

\frac{1}{3} arctan (3 x) + C

Solution steps

\int \frac{1}{9 x ^{2} + 1} d x

Apply Integral Substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 3 x

= \frac{1}{3} arctan (3 x)

Add a constant to the solution

= \frac{1}{3} arctan (3 x) + C

Popular Examples

integral of sin(x

\int sin (d) x d x

derivative of (x^3+1/(x^3-1))

\frac{d}{d x} (\frac{x ^{3} + 1}{x ^{3} - 1})

integral of (x-1)sqrt(2-x)

\int (x - 1) 2 - x d x

limit as x approaches 3 of (f(x)-f(pi))/(sqrt(x)-\sqrt{3)}

x \to 3 lim (\frac{f ( x ) - f ( π )}{x - 3})

integral of (sqrt(x)-x+1)/(x^5)

\int \frac{x - x + 1}{x ^{5}} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(9x^2+1) ?
The integral of 1/(9x^2+1) is 1/3 arctan(3x)+C