What is the integral of e^{2xy} ?

The integral of e^{2xy} is 1/(2y)e^{2yx}+C

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integral of e^{2xy}

\int e^{2 x y} d x

\frac{1}{2 y} e^{2 y x} + C

Solution steps

\int e^{2 x y} d x

Apply u-substitution

: \int \frac{e ^{u}}{2 y} d u

= \int \frac{e ^{u}}{2 y} d u

Take the constant out:

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

= \frac{1}{2 y} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2 y} e^{u}

Substitute back

u = 2 y x

= \frac{1}{2 y} e^{2 y x}

Add a constant to the solution

= \frac{1}{2 y} e^{2 y x} + C

\int cos (2 x) cos (x) d x

\int \frac{x}{( x ^{4} + 1 )} d x

\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6}

h \to 0 lim (\frac{( f ( h ) ( 0 + h ) - f ( 0 ) )}{h})