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Popular >

integral of 2xe^y

Solution

\int 2 x e^{y} d x

Solution

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

Solution steps

\int 2 x e^{y} d x

Take the constant out:

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

= 2 e^{y} \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

= e^{y} x^{2}

Add a constant to the solution

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

Popular Examples

derivative of f(x)=((x+3)(x+1))/(x^2-49)derivative of

f (x) = \frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49}

derivative of y=ln(x+sqrt(x^2+6))derivative of

y = ln (x + x^{2} + 6)

taylor x^{1/4},16 taylor

x^{\frac{1}{4}}, 16

derivative of (ln(-2x^3+5x^2)/(-x))

\frac{d}{d x} (\frac{ln ( - 2 x ^{3} + 5 x ^{2} )}{- x})

f (x) = \frac{1}{1 + x}

Frequently Asked Questions (FAQ)

What is the integral of 2xe^y ?
The integral of 2xe^y is e^yx^2+C