What is expand 2pi(x)(x^{1/2}-3)dx ?

The solution to expand 2pi(x)(x^{1/2}-3)dx is 2pix^{3/2}dx-6pixdx

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expand 2pi(x)(x^{1/2}-3)dx

expand

2 π (x) (x^{\frac{1}{2}} - 3) d x

2 π x^{\frac{3}{2}} d x - 6 π x d x

Solution steps

2 π (x) (x^{\frac{1}{2}} - 3) d x

Apply the distributive law:

a (b - c) = ab - a c

a = 2 π (x) d x, b = x^{\frac{1}{2}}, c = 3

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

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

Simplify

2 π (x) x^{\frac{1}{2}} d x - 2 \cdot 3 π (x) d x : 2 π x^{\frac{3}{2}} d x - 6 π x d x

= 2 π x^{\frac{3}{2}} d x - 6 π x d x

d H (x^{2} + 1)

\frac{1}{( 1 + 3 x ) ^{5}}

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

\frac{2 x ^{2} + 4 x + 1}{( x + 1 ) ( x + 2 ) ^{3}}

\frac{( e ^{5 x} - e ^{- 5 x} ) ^{2}}{4}

What is expand 2pi(x)(x^{1/2}-3)dx ?
The solution to expand 2pi(x)(x^{1/2}-3)dx is 2pix^{3/2}dx-6pixdx