What is the integral of (21t^2-10t)/(7t^3-5t^2+13) ?

The integral of (21t^2-10t)/(7t^3-5t^2+13) is ln|7t^3-5t^2+13|+C

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integral of (21t^2-10t)/(7t^3-5t^2+13)

\int \frac{21 t ^{2} - 10 t}{7 t ^{3} - 5 t ^{2} + 13} d t

ln 7 t^{3} - 5 t^{2} + 13 + C

Solution steps

\int \frac{21 t ^{2} - 10 t}{7 t ^{3} - 5 t ^{2} + 13} d t

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 7 t^{3} - 5 t^{2} + 13

= ln 7 t^{3} - 5 t^{2} + 13

Add a constant to the solution

= ln 7 t^{3} - 5 t^{2} + 13 + C

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What is the integral of (21t^2-10t)/(7t^3-5t^2+13) ?
The integral of (21t^2-10t)/(7t^3-5t^2+13) is ln|7t^3-5t^2+13|+C