What is the integral of x/(x^2+49) ?

The integral of x/(x^2+49) is 1/2 ln|x^2+49|+C

Popular >

integral of x/(x^2+49)

\int \frac{x}{x ^{2} + 49} d x

\frac{1}{2} ln x^{2} + 49 + C

Solution steps

\int \frac{x}{x ^{2} + 49} 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 = x^{2} + 49

= \frac{1}{2} ln x^{2} + 49

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 49 + C

\frac{1}{( s - 3 ) ( s - 9 )}

(x, y) \to (0, 0) lim (\frac{( sin ( 2 x ) - 2 x + y )}{x ^{3} + y})

\int ln (x) \cdot ln (x) d x

y^{^{''}} x = - 5 sin (8 x)

\frac{\partial}{\partial x} (x ln (z^{7} + x^{5}))

What is the integral of x/(x^2+49) ?
The integral of x/(x^2+49) is 1/2 ln|x^2+49|+C