What is the integral of sqrt(m+nx) ?

The integral of sqrt(m+nx) is (2(m+nx)^{3/2})/(3n)+C

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integral of sqrt(m+nx)

\int m + n x d x

\frac{2 ( m + n x ) ^{\frac{3}{2}}}{3 n} + C

Solution steps

\int m + n x d x

Apply u-substitution

: \int \frac{u}{n} d u

= \int \frac{u}{n} d u

Take the constant out:

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

= \frac{1}{n} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{n} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = m + n x

= \frac{1}{n} \cdot \frac{2}{3} (m + n x)^{\frac{3}{2}}

Simplify

\frac{1}{n} \cdot \frac{2}{3} (m + n x)^{\frac{3}{2}} : \frac{2 ( m + n x ) ^{\frac{3}{2}}}{3 n}

= \frac{2 ( m + n x ) ^{\frac{3}{2}}}{3 n}

Add a constant to the solution

= \frac{2 ( m + n x ) ^{\frac{3}{2}}}{3 n} + C

\frac{d}{d x} ((1 - 5 x)^{- 2})

y = e^{3 x} cos (π x), (0, 1)

\frac{\partial}{\partial y} (sin (yz))

\int - \frac{2 x}{( x ^{2} - 2 ) ^{3}} d x

\int \frac{2 x ^{2} - x + 3}{x} d x

What is the integral of sqrt(m+nx) ?
The integral of sqrt(m+nx) is (2(m+nx)^{3/2})/(3n)+C