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Popular >

integral of (2t+3)/t

Solution

\int \frac{2 t + 3}{t} d t

Solution

2 t + 3 ln ∣ t ∣ + C

Solution steps

\int \frac{2 t + 3}{t} d t

Expand

\frac{2 t + 3}{t} : 2 + \frac{3}{t}

= \int 2 + \frac{3}{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 2 d t + \int \frac{3}{t} d t

\int 2 d t = 2 t

\int \frac{3}{t} d t = 3 ln ∣ t ∣

= 2 t + 3 ln ∣ t ∣

Add a constant to the solution

= 2 t + 3 ln ∣ t ∣ + C

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\int \frac{10 x ^{2}}{8 + 9 x} d x

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\int (x^{3} + 1)^{10} x^{2} d x

integral of ((x^4+2x^2-1)/(sqrt(x)))

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

Frequently Asked Questions (FAQ)

What is the integral of (2t+3)/t ?
The integral of (2t+3)/t is 2t+3ln|t|+C