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Popular Calculus >

integral of (2x+e^y)

Solution

\int (2 x + e^{y}) d x

Solution

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

Solution steps

\int 2 x + e^{y} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 2 x d x = x^{2}

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

Add a constant to the solution

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

Graph

Popular Examples

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\int sin (\frac{nπ x}{20}) d x

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\int (sec^{2} (θ) tan^{3} (θ)) d θ

integral of 3/(sqrt(x+1)+\sqrt{x)}

\int \frac{3}{x + 1 + x} d x

integral of 1/t sin(ln(c/t))

\int \frac{1}{t} sin (ln (\frac{c}{t})) d t

integral of (e^{x/2})/(sqrt(1-e^x))

\int \frac{e ^{\frac{x}{2}}}{1 - e ^{x}} d x

Frequently Asked Questions (FAQ)

What is the integral of (2x+e^y) ?
The integral of (2x+e^y) is e^yx+x^2+C