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Popular >

integral of 1/(5+u)

Solution

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

Solution

ln ∣ 5 + u ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

v = 5 + u

= ln ∣ 5 + u ∣

Add a constant to the solution

= ln ∣ 5 + u ∣ + C

Popular Examples

integral of 1/9 xe^{-x/3}

\int \frac{1}{9} x e^{- \frac{x}{3}} d x

integral of (1/(x^2)+5x-2)

\int (\frac{1}{x ^{2}} + 5 x - 2) d x

integral of sin(8x)sec^5(8x)

\int sin (8 x) sec^{5} (8 x) d x

integral of tan^2(arctan(x)

\int tan^{2} (arctan (d) x) d x

integral of (1+2x)^{1/2}

\int (1 + 2 x)^{\frac{1}{2}} d x

Frequently Asked Questions (FAQ)

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