What is the integral from 0 to 1 of $x \cdot \sqrt{x^{2} + 8}$ $x*sqrt(x^2+8)$ ?

Question

What is the integral from 0 to 1 of $x \cdot \sqrt{x^{2} + 8}$ $x*sqrt(x^2+8)$ ?

1 Answer

Related questions

How do you find the integral $\int \frac{1}{x^{2} \cdot \sqrt{x^{2} - 9}} d x$ $int1/(x^2*sqrt(x^2-9))dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{x^{2} + 9}} d x$ $intx^3/(sqrt(x^2+9))dx$ ?
How do you find the integral $\int x^{3} \cdot \sqrt{9 - x^{2}} d x$ $intx^3*sqrt(9-x^2)dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{16 - x^{2}}} d x$ $intx^3/(sqrt(16-x^2))dx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 1}}{x} d x$ $intsqrt(x^2-1)/xdx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 9}}{x^{3}} d x$ $intsqrt(x^2-9)/x^3dx$ ?
How do you find the integral $\int \frac{x}{\sqrt{x^{2} + x + 1}} d x$ $intx/(sqrt(x^2+x+1))dx$ ?
How do you find the integral $\int \frac{d t}{\sqrt{t^{2} - 6 t + 13}}$ $intdt/(sqrt(t^2-6t+13))$ ?
How do you find the integral $\int x \cdot \sqrt{1 - x^{4}} d x$ $intx*sqrt(1-x^4)dx$ ?
How do you prove the integral formula $\int \frac{d x}{\sqrt{x^{2} + a^{2}}} = ln (x + \sqrt{x^{2} + a^{2}}) + C$ $intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C$ ?

Impact of this question

1752 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-06T22:06:56

Try this:
$\int x \sqrt{x^{2} + 8} d x =$ $intxsqrt(x^2+8)dx=$
But $d [x^{2} + 8] = 2 x d x$ $d[x^2+8]=2xdx$
So:
$\frac{1}{2} \int \sqrt{x^{2} + 8} d [x^{2} + 8] =$ $1/2intsqrt(x^2+8)d[x^2+8]=$
$= \frac{1}{2} \int {(x^{2} + 8)}^{\frac{1}{2}} d [x^{2} + 8] = \frac{1}{2} \frac{{(x^{2} + 8)}^{\frac{3}{2}}}{\frac{3}{2}}$ $=1/2int(x^2+8)^(1/2)d[x^2+8]=1/2((x^2+8)^(3/2))/(3/2)$
Between $0$ $0$ and $1$ $1$ :
$= \frac{1}{3} {(x^{2} + 8)}^{\frac{3}{2}} {∣ ∣ ∣}_{0}^{1}$ $=1/3(x^2+8)^(3/2)|_0^1$ = $9 - \frac{8}{3} \sqrt{8} = 9 - \frac{16}{3} \sqrt{2}$ $9-8/3sqrt(8)=9-16/3sqrt(2)$

Science

Math

Humanities

... and beyond

What is the integral from 0 to 1 of $x \cdot \sqrt{x^{2} + 8}$ $x*sqrt(x^2+8)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the integral from 0 to 1 of x⋅√x2+8x*sqrt(x^2+8)?

1 Answer

Related questions

Impact of this question

What is the integral from 0 to 1 of $x \cdot \sqrt{x^{2} + 8}$ $x*sqrt(x^2+8)$ ?