en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of f(g(x))

Solution

\int f (g (x))

Solution

\frac{gx f ^{2}}{2} + C

Solution steps

\int f gx df

Take the constant out:

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

= gx \cdot \int fdf

Apply the Power Rule

= gx \frac{f ^{2}}{2}

Multiply fractions:

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

= \frac{gx f ^{2}}{2}

Add a constant to the solution

= \frac{gx f ^{2}}{2} + C

Graph

Popular Examples

integral from 0 to 2 of 1/(sqrt(x))

\int_{0}^{2} \frac{1}{x} d x

derivative of sin^n(x)

\frac{d}{d x} (sin^{n} (x))

4xy^3y^'=x^4+4y^4

4 x y^{3} y^{^{'}} = x^{4} + 4 y^{4}

integral of sqrt(49-x^2)

\int 49 - x^{2} d x

integral of (x^5-x^3+8x)/(x^4)

\int \frac{x ^{5} - x ^{3} + 8 x}{x ^{4}} d x

Frequently Asked Questions (FAQ)

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