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Popular >

integral of (t-4)/t

Solution

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

Solution

t - 4 ln ∣ t ∣ + C

Solution steps

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

Expand

\frac{t - 4}{t} : 1 - \frac{4}{t}

= \int 1 - \frac{4}{t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d t - \int \frac{4}{t} d t

\int 1 d t = t

\int \frac{4}{t} d t = 4 ln ∣ t ∣

= t - 4 ln ∣ t ∣

Add a constant to the solution

= t - 4 ln ∣ t ∣ + C

Popular Examples

integral of (e^{2x})/(36+e^{2x)}

\int \frac{e ^{2 x}}{36 + e ^{2 x}} d x

integral of sqrt(30x-9x^2-21)

\int 30 x - 9 x^{2} - 21 d x

integral of 1/(x^4+x^6)

\int \frac{1}{x ^{4} + x ^{6}} d x

integral of (x^2+x)*e^{1-2x}

\int (x^{2} + x) \cdot e^{1 - 2 x} d x

integral of 1/(36+9x^2)

\int \frac{1}{36 + 9 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (t-4)/t ?
The integral of (t-4)/t is t-4ln|t|+C