What is the integral from 0 to 2 of sqrt(144x+577) ?

The integral from 0 to 2 of sqrt(144x+577) is (865sqrt(865)-577sqrt(577))/(216)

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integral from 0 to 2 of sqrt(144x+577)

\int_{0}^{2} 144 x + 577 d x

\frac{865 865 - 577 577}{216}

Decimal Notation

53.61295 \dots

Solution steps

\int_{0}^{2} 144 x + 577 d x

Apply u-substitution

: \int_{577}^{865} \frac{u}{144} d u

= \int_{577}^{865} \frac{u}{144} d u

Take the constant out:

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

= \frac{1}{144} \cdot \int_{577}^{865} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{577}^{865}

= \frac{1}{144} [\frac{2}{3} u^{\frac{3}{2}}]_{577}^{865}

Compute the boundaries:

\frac{1730 865 - 1154 577}{3}

= \frac{1}{144} \cdot \frac{1730 865 - 1154 577}{3}

Simplify

= \frac{865 865 - 577 577}{216}

\frac{81}{8 ( 3 x + 2 ) ^{\frac{5}{2}}}

\int 2 x + \frac{4}{x} d x

\frac{\partial}{\partial x} (5 x + 10 y + 10 x y)

4 t \frac{d y}{d t} + 22 y = 0

n = 1 \sum \infty \frac{n}{n}

What is the integral from 0 to 2 of sqrt(144x+577) ?
The integral from 0 to 2 of sqrt(144x+577) is (865sqrt(865)-577sqrt(577))/(216)