What is the integral of 3(2x-3)^4 ?

The integral of 3(2x-3)^4 is 3/10 (2x-3)^5+C

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integral of 3(2x-3)^4

\int 3 (2 x - 3)^{4} d x

\frac{3}{10} (2 x - 3)^{5} + C

Solution steps

\int 3 (2 x - 3)^{4} d x

Take the constant out:

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

= 3 \cdot \int (2 x - 3)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= 3 \cdot \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 3 \cdot \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = 2 x - 3

= 3 \cdot \frac{1}{2} \cdot \frac{( 2 x - 3 ) ^{5}}{5}

Simplify

3 \cdot \frac{1}{2} \cdot \frac{( 2 x - 3 ) ^{5}}{5} : \frac{3}{10} (2 x - 3)^{5}

= \frac{3}{10} (2 x - 3)^{5}

Add a constant to the solution

= \frac{3}{10} (2 x - 3)^{5} + C

\int 2 x - 10 d x

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\int \frac{1}{2 v} d v

What is the integral of 3(2x-3)^4 ?
The integral of 3(2x-3)^4 is 3/10 (2x-3)^5+C