What is the integral of x/(a^2+x^2) ?

The integral of x/(a^2+x^2) is 1/2 ln|a^2+x^2|+C

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integral of x/(a^2+x^2)

\int \frac{x}{a ^{2} + x ^{2}} d x

\frac{1}{2} ln a^{2} + x^{2} + C

Solution steps

\int \frac{x}{a ^{2} + x ^{2}} d x

Apply u-substitution

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

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = a^{2} + x^{2}

= \frac{1}{2} ln a^{2} + x^{2}

Add a constant to the solution

= \frac{1}{2} ln a^{2} + x^{2} + C

\frac{d}{d x} (x y + 8)

h \to 0 lim (4 h - h^{2})

\int \frac{9 - 162 x}{25 - 81 x ^{2}} d x

n = 0 \sum \infty (n + 1)!

x \to 0 + lim (3 ln (x) + \frac{5}{x})

What is the integral of x/(a^2+x^2) ?
The integral of x/(a^2+x^2) is 1/2 ln|a^2+x^2|+C