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Popular >

integral of 1/(5+t)

Solution

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

Solution

ln ∣ 5 + t ∣ + C

Solution steps

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

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 + t

= ln ∣ 5 + t ∣

Add a constant to the solution

= ln ∣ 5 + t ∣ + C

Popular Examples

integral of (sqrt(t^2-4))/t

\int \frac{t ^{2} - 4}{t} d t

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\int t cos (n) t d t

integral of (1+4x^2)^{3/2}

\int (1 + 4 x^{2})^{\frac{3}{2}} d x

integral of (24x^5-12x^3-x+2)

\int (24 x^{5} - 12 x^{3} - x + 2) d x

integral of (3x^2+5)/(x^3+5x+2)

\int \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 2} d x

Frequently Asked Questions (FAQ)

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