en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of f(x+b)

Solution

\int f (x + b) d x

Solution

f (b x + \frac{x ^{2}}{2}) + C

Solution steps

\int f (x + b) d x

Take the constant out:

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

= f \cdot \int b + x 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

= f (\int b d x + \int x d x)

\int b d x = b x

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

= f (b x + \frac{x ^{2}}{2})

Add a constant to the solution

= f (b x + \frac{x ^{2}}{2}) + C

Graph

Popular Examples

derivative of sqrt(x+2)derivative of

x + 2

tangent of 2x^3-4x^2,\at x=1 tangent of

2 x^{3} - 4 x^{2}, at x = 1

integral of 14ln(\sqrt[3]{x})

\int 14 ln (3 x) d x

derivative of y= 7/x+6sec(x)derivative of

y = \frac{7}{x} + 6 sec (x)

(\partial)/(\partial y)((3x)/((x+y)^4))

\frac{\partial}{\partial y} (\frac{3 x}{( x + y ) ^{4}})

Frequently Asked Questions (FAQ)

What is the integral of f(x+b) ?
The integral of f(x+b) is f(bx+(x^2)/2)+C