What is the integral of (x+2y+3z)^2 ?

The integral of (x+2y+3z)^2 is 2yx^2+3zx^2+(x^3)/3+4y^2x+12yzx+9z^2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+2y+3z)^2

\int (x + 2 y + 3 z)^{2} d x

2 y x^{2} + 3 z x^{2} + \frac{x ^{3}}{3} + 4 y^{2} x + 12 yz x + 9 z^{2} x + C

Solution steps

\int (x + 2 y + 3 z)^{2} d x

Expand

(x + 2 y + 3 z)^{2} : 4 y x + 6 z x + x^{2} + 4 y^{2} + 12 yz + 9 z^{2}

= \int 4 y x + 6 z x + x^{2} + 4 y^{2} + 12 yz + 9 z^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 y x d x + \int 6 z x d x + \int x^{2} d x + \int 4 y^{2} d x + \int 12 yz d x + \int 9 z^{2} d x

\int 4 y x d x = 2 y x^{2}

\int 6 z x d x = 3 z x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

\int 4 y^{2} d x = 4 y^{2} x

\int 12 yz d x = 12 yz x

\int 9 z^{2} d x = 9 z^{2} x

= 2 y x^{2} + 3 z x^{2} + \frac{x ^{3}}{3} + 4 y^{2} x + 12 yz x + 9 z^{2} x

Add a constant to the solution

= 2 y x^{2} + 3 z x^{2} + \frac{x ^{3}}{3} + 4 y^{2} x + 12 yz x + 9 z^{2} x + C

\int r^{2} - x^{2} d x

\frac{d}{d x} (4 - 3 x)

(19 x y^{2} + 11 y) + (19 x^{2} y + 11 x) (\frac{d y}{d x}) = 0

y^{^{''}} + 4 y = sec (2 x)

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

What is the integral of (x+2y+3z)^2 ?
The integral of (x+2y+3z)^2 is 2yx^2+3zx^2+(x^3)/3+4y^2x+12yzx+9z^2x+C