What is the integral of (t^2)/(t^3-pi^3) ?

The integral of (t^2)/(t^3-pi^3) is 1/3 ln|t^3-pi^3|+C

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integral of (t^2)/(t^3-pi^3)

\int \frac{t ^{2}}{t ^{3} - π ^{3}} d t

\frac{1}{3} ln t^{3} - π^{3} + C

Solution steps

\int \frac{t ^{2}}{t ^{3} - π ^{3}} d t

Apply u-substitution

= \int \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = t^{3} - π^{3}

= \frac{1}{3} ln t^{3} - π^{3}

Add a constant to the solution

= \frac{1}{3} ln t^{3} - π^{3} + C

What is the integral of (t^2)/(t^3-pi^3) ?
The integral of (t^2)/(t^3-pi^3) is 1/3 ln|t^3-pi^3|+C