What is the integral of (t^2)/((a+bt^3)^2) ?

The integral of (t^2)/((a+bt^3)^2) is -1/(3b(a+bt^3))+C

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integral of (t^2)/((a+bt^3)^2)

\int \frac{t ^{2}}{( a + b t ^{3} ) ^{2}} d t

- \frac{1}{3 b ( a + b t ^{3} )} + C

Solution steps

\int \frac{t ^{2}}{( a + b t ^{3} ) ^{2}} d t

Apply u-substitution

= \int \frac{1}{3 b u ^{2}} d u

Take the constant out:

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

= \frac{1}{3 b} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= \frac{1}{3 b} (- \frac{1}{u})

Substitute back

u = a + b t^{3}

= \frac{1}{3 b} (- \frac{1}{a + b t ^{3}})

Simplify

\frac{1}{3 b} (- \frac{1}{a + b t ^{3}}) : - \frac{1}{3 b ( a + b t ^{3} )}

= - \frac{1}{3 b ( a + b t ^{3} )}

Add a constant to the solution

= - \frac{1}{3 b ( a + b t ^{3} )} + C

x y^{^{'}} = 2 x^{2} y + 3 x^{3} e^{x^{2}}

\int_{4}^{9} \frac{1}{5 - x} d x

\int x^{2} x - 5 d x

x \to \infty lim (x ln (1))

\frac{2 x - 5}{x}

What is the integral of (t^2)/((a+bt^3)^2) ?
The integral of (t^2)/((a+bt^3)^2) is -1/(3b(a+bt^3))+C