en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of y(4+y^2)

Solution

\int y (4 + y^{2}) d y

Solution

2 y^{2} + \frac{y ^{4}}{4} + C

Solution steps

\int y (4 + y^{2}) d y

Expand

y (4 + y^{2}) : 4 y + y^{3}

= \int 4 y + y^{3} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 y d y + \int y^{3} d y

\int 4 y d y = 2 y^{2}

\int y^{3} d y = \frac{y ^{4}}{4}

= 2 y^{2} + \frac{y ^{4}}{4}

Add a constant to the solution

= 2 y^{2} + \frac{y ^{4}}{4} + C

Popular Examples

integral of (2x-9)/(sqrt(x^2-9x+5))

\int \frac{2 x - 9}{x ^{2} - 9 x + 5} d x

integral of 2sin^5(x)cos^4(x)

\int 2 sin^{5} (x) cos^{4} (x) d x

integral of 1/2 cot^3(x)csc(x)

\int \frac{1}{2} cot^{3} (x) csc (x) d x

integral of x^3(x^2+4)^{1/2}

\int x^{3} (x^{2} + 4)^{\frac{1}{2}} d x

integral of (z^4)/(sqrt(1-z^{10))}

\int \frac{z ^{4}}{1 - z ^{10}} d z

Frequently Asked Questions (FAQ)

What is the integral of y(4+y^2) ?
The integral of y(4+y^2) is 2y^2+(y^4)/4+C