What is the integral of x^4sqrt(10+x^5) ?

The integral of x^4sqrt(10+x^5) is 2/15 (10+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(10+x^5)

\int x^{4} 10 + x^{5} d x

\frac{2}{15} (10 + x^{5})^{\frac{3}{2}} + C

Solution steps

\int x^{4} 10 + 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 = 10 + x^{5}

= \frac{1}{5} \cdot \frac{2}{3} (10 + x^{5})^{\frac{3}{2}}

Simplify

\frac{1}{5} \cdot \frac{2}{3} (10 + x^{5})^{\frac{3}{2}} : \frac{2}{15} (10 + x^{5})^{\frac{3}{2}}

= \frac{2}{15} (10 + x^{5})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{15} (10 + x^{5})^{\frac{3}{2}} + C

\int (x + 3)^{7} d x

\int \frac{5}{7 x} d x

\int \frac{x}{225 x ^{2} - 1} d x

\int \frac{x ^{2} e ^{x}}{( 2 + x ) ^{2}} d x

\int \frac{1}{5 - 9 y} d y

What is the integral of x^4sqrt(10+x^5) ?
The integral of x^4sqrt(10+x^5) is 2/15 (10+x^5)^{3/2}+C