What is the integral of (3t^2)/(sqrt(t^3+5)) ?

The integral of (3t^2)/(sqrt(t^3+5)) is 2sqrt(t^3+5)+C

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integral of (3t^2)/(sqrt(t^3+5))

\int \frac{3 t ^{2}}{t ^{3} + 5} d t

2 t^{3} + 5 + C

Solution steps

\int \frac{3 t ^{2}}{t ^{3} + 5} d t

Take the constant out:

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

= 3 \cdot \int \frac{t ^{2}}{t ^{3} + 5} d t

Apply u-substitution

: \int \frac{2}{3} d u

= 3 \cdot \int \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= 3 \cdot \frac{2}{3} u

Substitute back

u = t^{3} + 5

= 3 \cdot \frac{2}{3} t^{3} + 5

Simplify

3 \cdot \frac{2}{3} t^{3} + 5 : 2 t^{3} + 5

= 2 t^{3} + 5

Add a constant to the solution

= 2 t^{3} + 5 + C

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\int_{0}^{π} sin^{2} (x co) s^{4} x d x

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x \to - 7 + lim (\frac{x - 4}{x + 7})

What is the integral of (3t^2)/(sqrt(t^3+5)) ?
The integral of (3t^2)/(sqrt(t^3+5)) is 2sqrt(t^3+5)+C