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

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

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integral of x/(a+bx^2)

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2 b} ln ∣ u ∣

Substitute back

u = a + b x^{2}

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

Add a constant to the solution

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

\frac{d}{d x} (x^{3} + x^{5})

\frac{d}{d x} (i n^{4} x)

x^{2} - x + 1

\frac{\partial}{\partial x} (2 x)

y = \frac{2}{( x - 8 ) , at ( 10 , 1 )}

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