What is the integral of (4/(3t^2)+7/(2t)) ?

The integral of (4/(3t^2)+7/(2t)) is -4/(3t)+7/2 ln|t|+C

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integral of (4/(3t^2)+7/(2t))

\int (\frac{4}{3 t ^{2}} + \frac{7}{2 t}) d t

- \frac{4}{3 t} + \frac{7}{2} ln ∣ t ∣ + C

Solution steps

\int \frac{4}{3 t ^{2}} + \frac{7}{2 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 \frac{4}{3 t ^{2}} d t + \int \frac{7}{2 t} d t

\int \frac{4}{3 t ^{2}} d t = - \frac{4}{3 t}

\int \frac{7}{2 t} d t = \frac{7}{2} ln ∣ t ∣

= - \frac{4}{3 t} + \frac{7}{2} ln ∣ t ∣

Add a constant to the solution

= - \frac{4}{3 t} + \frac{7}{2} ln ∣ t ∣ + C

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\int \frac{1}{x ^{4} + 2 x ^{2} - 8} d x

\int - e^{- u} d u

\int (3 x^{2} - 6 x + 8) d x

What is the integral of (4/(3t^2)+7/(2t)) ?
The integral of (4/(3t^2)+7/(2t)) is -4/(3t)+7/2 ln|t|+C