What is the integral of 300(5y-3)^5 ?

The integral of 300(5y-3)^5 is 10(5y-3)^6+C

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integral of 300(5y-3)^5

\int 300 (5 y - 3)^{5} d y

10 (5 y - 3)^{6} + C

Solution steps

\int 300 (5 y - 3)^{5} d y

Take the constant out:

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

= 300 \cdot \int (5 y - 3)^{5} d y

Apply u-substitution

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

= 300 \cdot \int \frac{u ^{5}}{5} d u

Take the constant out:

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

= 300 \cdot \frac{1}{5} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 300 \cdot \frac{1}{5} \cdot \frac{u ^{6}}{6}

Substitute back

u = 5 y - 3

= 300 \cdot \frac{1}{5} \cdot \frac{( 5 y - 3 ) ^{6}}{6}

Simplify

300 \cdot \frac{1}{5} \cdot \frac{( 5 y - 3 ) ^{6}}{6} : 10 (5 y - 3)^{6}

= 10 (5 y - 3)^{6}

Add a constant to the solution

= 10 (5 y - 3)^{6} + C

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What is the integral of 300(5y-3)^5 ?
The integral of 300(5y-3)^5 is 10(5y-3)^6+C