What is expand (y^3+2y^2-1)/(sqrt(y))dy ?

The solution to expand (y^3+2y^2-1)/(sqrt(y))dy is (sqrt(y)(y^3dy+2y^2dy-dy))/y

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expand (y^3+2y^2-1)/(sqrt(y))dy

expand

\frac{y ^{3} + 2 y ^{2} - 1}{y} d y

\frac{y ( y ^{3} d y + 2 y ^{2} d y - d y )}{y}

Solution steps

\frac{y ^{3} + 2 y ^{2} - 1}{y} d y

Multiply fractions:

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

= \frac{( y ^{3} + 2 y ^{2} - 1 ) d y}{y}

Expand

(y^{3} + 2 y^{2} - 1) d y : y^{3} d y + 2 y^{2} d y - d y

= \frac{y ^{3} d y + 2 y ^{2} d y - d y}{y}

Rationalize

\frac{y ^{3} d y + 2 y ^{2} d y - d y}{y} : \frac{y ( y ^{3} d y + 2 y ^{2} d y - d y )}{y}

= \frac{y ( y ^{3} d y + 2 y ^{2} d y - d y )}{y}

\frac{d}{d z} ((f (z)) (z^{2} + 5))

(x + h)^{3} + 1 - x^{3} + 1

\frac{( 2 s + 4 )}{( s - 2 ) ( s ^{2} + 4 s + 3 )}

\frac{2 x}{( 1 - ( 1 - x ) ^{2} ) ^{2}}

\frac{5 ( 8 + 19 )}{6}

What is expand (y^3+2y^2-1)/(sqrt(y))dy ?
The solution to expand (y^3+2y^2-1)/(sqrt(y))dy is (sqrt(y)(y^3dy+2y^2dy-dy))/y