en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xin^2x

Solution

\int x i n^{2} x d x

Solution

\frac{i n ^{2} x ^{3}}{3} + C

Solution steps

\int x i n^{2} x d x

Take the constant out:

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

= i n^{2} \cdot \int xx d x

Simplify

xx : x^{2}

= i n^{2} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= i n^{2} \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{i n ^{2} x ^{3}}{3}

Add a constant to the solution

= \frac{i n ^{2} x ^{3}}{3} + C

Popular Examples

integral of (sqrt(x^2-81))/(x^3)

\int \frac{x ^{2} - 81}{x ^{3}} d x

integral of+x/(3x^2+1)

\int + \frac{x}{3 x ^{2} + 1} d x

derivative of (2x^3+5^{10})

\frac{d}{d x} ((2 x^{3} + 5)^{10})

integral of sec(x)

\int sec (x) d x

derivative of (e^x/x+ln(x))

\frac{d}{d x} (\frac{e ^{x}}{x} + ln (x))

Frequently Asked Questions (FAQ)

What is the integral of xin^2x ?
The integral of xin^2x is (in^2x^3)/3+C