What is the integral of e^{sqrt(2x)} ?

The integral of e^{sqrt(2x)} is sqrt(2)e^{sqrt(2)sqrt(x)}sqrt(x)-e^{sqrt(2)sqrt(x)}+C

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integral of e^{sqrt(2x)}

\int e^{2 x} d x

2 e^{2 x} x - e^{2 x} + C

Solution steps

\int e^{2 x} d x

Apply u-substitution

: \int e^{u} u d u

= \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= e^{u} u - \int e^{u} d u

\int e^{u} d u = e^{u}

= e^{u} u - e^{u}

Substitute back

u = 2 x

= e^{2 x} 2 x - e^{2 x}

Simplify

e^{2 x} 2 x - e^{2 x} : 2 e^{2 x} x - e^{2 x}

= 2 e^{2 x} x - e^{2 x}

Add a constant to the solution

= 2 e^{2 x} x - e^{2 x} + C

\frac{d}{d x} (x^{5} (3 + 8 x)^{7})

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

\int_{2.3}^{2.75} 2 d x

y^{^{''}} + y^{^{'}} + y = 0.5 x

x^{2} y^{^{'}} = x y + x^{2} e^{\frac{y}{x}}

What is the integral of e^{sqrt(2x)} ?
The integral of e^{sqrt(2x)} is sqrt(2)e^{sqrt(2)sqrt(x)}sqrt(x)-e^{sqrt(2)sqrt(x)}+C