What is the integral of (Tg^5y^2)5y ?

The integral of (Tg^5y^2)5y is (5Tg^5y^4)/4+C

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integral of (Tg^5y^2)5y

\int (T g^{5} y^{2}) 5 y d y

\frac{5 T g ^{5} y ^{4}}{4} + C

Solution steps

\int T g^{5} y^{2} \cdot 5 y d y

Take the constant out:

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

= 5 T g^{5} \cdot \int y y^{2} d y

Simplify

y y^{2} : y^{3}

= 5 T g^{5} \cdot \int y^{3} d y

Apply the Power Rule

: \frac{y ^{4}}{4}

= 5 T g^{5} \frac{y ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 T g ^{5} y ^{4}}{4}

Add a constant to the solution

= \frac{5 T g ^{5} y ^{4}}{4} + C

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What is the integral of (Tg^5y^2)5y ?
The integral of (Tg^5y^2)5y is (5Tg^5y^4)/4+C