What is the integral of 4ye^{xy} ?

The integral of 4ye^{xy} is 4e^{yx}+C

Popular >

integral of 4ye^{xy}

\int 4 y e^{x y} d x

4 e^{y x} + C

Solution steps

\int 4 y e^{x y} d x

Take the constant out:

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

= 4 y \cdot \int e^{y x} d x

Apply u-substitution

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

= 4 y \cdot \int \frac{e ^{u}}{y} d u

Take the constant out:

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

= 4 y \frac{1}{y} \cdot \int e^{u} d u

Use the common integral:

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

= 4 y \frac{1}{y} e^{u}

Substitute back

u = y x

= 4 y \frac{1}{y} e^{y x}

Simplify

4 y \frac{1}{y} e^{y x} : 4 e^{y x}

= 4 e^{y x}

Add a constant to the solution

= 4 e^{y x} + C

\int \frac{x ^{2} + 3}{x ^{2} - 9} d x

\int \frac{x ^{3} - 4 x + 6}{x ^{2} + 3 x} d x

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

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

\int \frac{1}{x} \frac{x}{1 - x} d x