What is the integral from 1 to x of sqrt(1+2t) ?

The integral from 1 to x of sqrt(1+2t) is ((2x+1)^{3/2}-3sqrt(3))/3

Popular >

integral from 1 to x of sqrt(1+2t)

\int_{1}^{x} 1 + 2 t d t

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

Solution steps

\int_{1}^{x} 1 + 2 t d t

Apply u-substitution

: \int_{3}^{1 + 2 x} \frac{u}{2} d u

= \int_{3}^{1 + 2 x} \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{3}^{1 + 2 x} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{1 + 2 x}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{1 + 2 x}

Compute the boundaries:

\frac{2}{3} (1 + 2 x)^{\frac{3}{2}} - 23

= \frac{1}{2} (\frac{2}{3} (1 + 2 x)^{\frac{3}{2}} - 23)

Simplify

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

\frac{d}{d x} (\frac{4}{3} \cdot π \cdot x^{3})

\int x^{3} 5 x d x

x \to 0 lim (\frac{cos ( 6 x )}{1})

x \to 3 lim (\frac{2 x - 6}{x - 3})

\int_{0}^{π} x sin (n x) d x

What is the integral from 1 to x of sqrt(1+2t) ?
The integral from 1 to x of sqrt(1+2t) is ((2x+1)^{3/2}-3sqrt(3))/3