What is the integral of x(a-bx^2) ?

The integral of x(a-bx^2) is 1/2 x^2(a-bx^2)+(bx^4)/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(a-bx^2)

\int x (a - b x^{2}) d x

\frac{1}{2} x^{2} (a - b x^{2}) + \frac{b x ^{4}}{4} + C

Solution steps

\int x (a - b x^{2}) d x

Apply Integration By Parts

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

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

\int - b x^{3} d x = - \frac{b x ^{4}}{4}

= \frac{1}{2} x^{2} (a - b x^{2}) - (- \frac{b x ^{4}}{4})

Simplify

= \frac{1}{2} x^{2} (a - b x^{2}) + \frac{b x ^{4}}{4}

Add a constant to the solution

= \frac{1}{2} x^{2} (a - b x^{2}) + \frac{b x ^{4}}{4} + C

f (x) = 2 x^{2} + x - 2, at x = 4

\int \frac{- 1600 x}{25 - x ^{2}} d x

\int \frac{1}{x 8 x + 81} d x

\frac{\partial}{\partial x} (x + e^{y})

\frac{\partial}{\partial x} (4 x + 8 y - 88)

What is the integral of x(a-bx^2) ?
The integral of x(a-bx^2) is 1/2 x^2(a-bx^2)+(bx^4)/4+C