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Popular >

integral of 1/(1+t)

Solution

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

Solution

ln ∣ 1 + t ∣ + C

Solution steps

\int \frac{1}{1 + 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 = 1 + t

= ln ∣ 1 + t ∣

Add a constant to the solution

= ln ∣ 1 + t ∣ + C

Popular Examples

derivative of (4x)/(x^2+4)derivative of

\frac{4 x}{x ^{2} + 4}

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\int e^{x^{2}} 4 x d x

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\int_{1}^{3} x^{2} d x

limit as x approaches 4+of (-3)/(8-2x)

x \to 4 + lim (\frac{- 3}{8 - 2 x})

derivative of 6x^{1.5}-4x^{0.5}

\frac{d}{d x} (6 x^{1.5} - 4 x^{0.5})

Frequently Asked Questions (FAQ)

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