What is the integral of 1^{22}x*sqrt(x^2-11) ?

The integral of 1^{22}x*sqrt(x^2-11) is 1/3 (x^2-11)^{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 1^{22}x*sqrt(x^2-11)

integral

1^{22} x \cdot x^{2} - 11

\frac{1}{3} (x^{2} - 11)^{\frac{3}{2}} + C

Solution steps

\int 1^{22} x x^{2} - 11 d x

Take the constant out:

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

= 1^{22} \cdot \int x x^{2} - 11 d x

Simplify

= 1 \cdot \int x x^{2} - 11 d x

Apply u-substitution

: \int u^{2} d u

= 1 \cdot \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = x^{2} - 11

= 1 \cdot \frac{( x ^{2} - 11 ) ^{3}}{3}

Simplify

1 \cdot \frac{( x ^{2} - 11 ) ^{3}}{3} : \frac{1}{3} (x^{2} - 11)^{\frac{3}{2}}

= \frac{1}{3} (x^{2} - 11)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (x^{2} - 11)^{\frac{3}{2}} + C

f (x) = x^{3} (3 x^{5} - 10)^{11}

\frac{x}{a ^{2}}

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

\frac{4 x}{x ^{2} + 1}

\frac{x ^{2}}{x ^{2} + 21}

What is the integral of 1^{22}x*sqrt(x^2-11) ?
The integral of 1^{22}x*sqrt(x^2-11) is 1/3 (x^2-11)^{3/2}+C