en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xln(x^3)

Solution

\int x ln (x^{3}) d x

Solution

\frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4} + C

Solution steps

\int x ln (x^{3}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{3}) - \int \frac{3 x}{2} d x

= \frac{1}{2} x^{2} ln (x^{3}) - \int \frac{3 x}{2} d x

\int \frac{3 x}{2} d x = \frac{3 x ^{2}}{4}

= \frac{1}{2} x^{2} ln (x^{3}) - \frac{3 x ^{2}}{4}

\frac{1}{2} x^{2} ln (x^{3}) = \frac{3}{2} x^{2} ln (x)

= \frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4}

Add a constant to the solution

= \frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4} + C

Popular Examples

(\partial)/(\partial x)((2x-y)/(x+4y))

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 4 y})

integral of e^{cos(t)}

\int e^{c o s (t)} d t

derivative of (x-3)^{-2}derivative of

(x - 3)^{- 2}

(dy)/(dx)=(e^x)/(y^2)

\frac{d y}{d x} = \frac{e ^{x}}{y ^{2}}

integral of (x^2)/(e^x)

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

Frequently Asked Questions (FAQ)

What is the integral of xln(x^3) ?
The integral of xln(x^3) is 3/2 x^2ln(x)-(3x^2)/4+C