What is the integral of 5/t ?

The integral of 5/t is 5ln|t|+C

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integral of 5/t

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

5 ln ∣ t ∣ + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 5 ln ∣ t ∣

Add a constant to the solution

= 5 ln ∣ t ∣ + C

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

y = \frac{3 x}{2 ^{x}}, at x = 2

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

(\frac{x ^{2} - 2}{5 x ^{3} + 6})^{^{'}}

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = 10