What is the integral of (12x)/(e^2-e^{2y^2)} ?

The integral of (12x)/(e^2-e^{2y^2)} is (6x^2)/(-e^{2y^2)+e^2}+C

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integral of (12x)/(e^2-e^{2y^2)}

\int \frac{12 x}{e ^{2} - e ^{2 y^{2}}} d x

\frac{6 x ^{2}}{- e ^{2 y^{2}} + e ^{2}} + C

Solution steps

\int \frac{12 x}{e ^{2} - e ^{2 y^{2}}} d x

Take the constant out:

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

= \frac{12}{- e ^{2 y^{2}} + e ^{2}} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{12}{- e ^{2 y^{2}} + e ^{2}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{12}{- e ^{2 y^{2}} + e ^{2}} \cdot \frac{x ^{2}}{2} : \frac{6 x ^{2}}{- e ^{2 y^{2}} + e ^{2}}

= \frac{6 x ^{2}}{- e ^{2 y^{2}} + e ^{2}}

Add a constant to the solution

= \frac{6 x ^{2}}{- e ^{2 y^{2}} + e ^{2}} + C

\int \frac{1}{( 4 y ) ^{2}} d y

f (x) = 6 sin (4 x)

(0, - 2), (3, 0)

\frac{e ^{1 - s}}{1 - s}

x \to \infty lim (x + \frac{3}{x})

What is the integral of (12x)/(e^2-e^{2y^2)} ?
The integral of (12x)/(e^2-e^{2y^2)} is (6x^2)/(-e^{2y^2)+e^2}+C