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Popular >

integral of 1/(5+x)

Solution

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

Solution

ln ∣ 5 + x ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 5 + x

= ln ∣ 5 + x ∣

Add a constant to the solution

= ln ∣ 5 + x ∣ + C

Popular Examples

sin(2x)dx+cos(5y)dy=0,y(pi/2)= pi/5

sin (2 x) d x + cos (5 y) d y = 0, y (\frac{π}{2}) = \frac{π}{5}

y^{''''}+20y^{''}+100y=0

y^{^{''''}} + 20 y^{^{''}} + 100 y = 0

derivative of 10x(x^2+3^4)

\frac{d}{d x} (10 x (x^{2} + 3)^{4})

derivative of-46xsin(x^2)derivative of

- 46 x sin (x^{2})

y^{^{'}} = e^{5 x + 3 y}

Frequently Asked Questions (FAQ)

What is the integral of 1/(5+x) ?
The integral of 1/(5+x) is ln|5+x|+C