What is the integral of x^4sqrt(4+x^5) ?

The integral of x^4sqrt(4+x^5) is 2/15 (4+x^5)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^4sqrt(4+x^5)

\int x^{4} 4 + x^{5} d x

\frac{2}{15} (4 + x^{5})^{\frac{3}{2}} + C

Solution steps

\int x^{4} 4 + x^{5} d x

Apply u-substitution

: \int \frac{u}{5} d u

= \int \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{5} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 4 + x^{5}

= \frac{1}{5} \cdot \frac{2}{3} (4 + x^{5})^{\frac{3}{2}}

Simplify

\frac{1}{5} \cdot \frac{2}{3} (4 + x^{5})^{\frac{3}{2}} : \frac{2}{15} (4 + x^{5})^{\frac{3}{2}}

= \frac{2}{15} (4 + x^{5})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{15} (4 + x^{5})^{\frac{3}{2}} + C

x \to 0 + lim (x^{2} + 3)

\frac{\partial}{\partial x} (9 x sin (8 x^{2} y))

e^{3 t} cos (2 t)

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

\int 3 x cos^{3} (x^{2} + 2) d x

What is the integral of x^4sqrt(4+x^5) ?
The integral of x^4sqrt(4+x^5) is 2/15 (4+x^5)^{3/2}+C