What is the integral of (3x+2)^{2.4} ?

The integral of (3x+2)^{2.4} is 0.09803…(3x+2)^{3.4}+C

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integral of (3x+2)^{2.4}

\int (3 x + 2)^{2.4} d x

0.09803 \dots (3 x + 2)^{3.4} + C

Solution steps

\int (3 x + 2)^{2.4} d x

Apply u-substitution

: \int \frac{u ^{2.4}}{3} d u

= \int \frac{u ^{2.4}}{3} 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 u^{2.4} d u

Apply the Power Rule

: 0.29411 \dots u^{3.4}

= \frac{1}{3} \cdot 0.29411 \dots u^{3.4}

Substitute back

u = 3 x + 2

= \frac{1}{3} \cdot 0.29411 \dots (3 x + 2)^{3.4}

Simplify

\frac{1}{3} \cdot 0.29411 \dots (3 x + 2)^{3.4} : 0.09803 \dots (3 x + 2)^{3.4}

= 0.09803 \dots (3 x + 2)^{3.4}

Add a constant to the solution

= 0.09803 \dots (3 x + 2)^{3.4} + C

\frac{\partial}{\partial x} (x^{6} y - 2 x^{5} y^{2})

- 2 x^{4} + 5 x^{2} - 3 (1)

y = e^{t}

x^{2} \frac{d y}{d x} = y

f (x) = 12 x, at x = 9

What is the integral of (3x+2)^{2.4} ?
The integral of (3x+2)^{2.4} is 0.09803…(3x+2)^{3.4}+C