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Popular >

integral of 1/(3t-1)

Solution

\int \frac{1}{3 t - 1} d t

Solution

\frac{1}{3} ln ∣ 3 t - 1 ∣ + C

Solution steps

\int \frac{1}{3 t - 1} d t

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = 3 t - 1

= \frac{1}{3} ln ∣ 3 t - 1 ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ 3 t - 1 ∣ + C

Popular Examples

limit as n approaches infinity of (3n^2+7n+11)/(8n^2-5n+3)

n \to \infty lim (\frac{3 n ^{2} + 7 n + 11}{8 n ^{2} - 5 n + 3})

integral of 4x+6

\int 4 x + 6 d x

integral of 5/(xsqrt(1-25ln^2(x)))

\int \frac{5}{x 1 - 25 ln ^{2} ( x )} d x

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

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

integral of 2/(x^3+1)

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

Frequently Asked Questions (FAQ)

What is the integral of 1/(3t-1) ?
The integral of 1/(3t-1) is 1/3 ln|3t-1|+C