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Popular >

integral of 1/(x+a)

Solution

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

Solution

ln ∣ x + a ∣ + C

Solution steps

\int \frac{1}{x + a} 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 = x + a

= ln ∣ x + a ∣

Add a constant to the solution

= ln ∣ x + a ∣ + C

Graph

Popular Examples

integral from 6 to 8 of 2pix(-3/2 x+12)

\int_{6}^{8} 2 π x (- \frac{3}{2} x + 12) d x

(\partial)/(\partial r)(rcos(x))

\frac{\partial}{\partial r} (r cos (x))

(dy)/(dx)=(x^2+3)/(3y)

\frac{d y}{d x} = \frac{x ^{2} + 3}{3 y}

derivative of f(x)=(ln(x))/(e^x)derivative of

f (x) = \frac{ln ( x )}{e ^{x}}

y^{^{''}} + 2 x y^{^{'}} = x

Frequently Asked Questions (FAQ)

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