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Popular >

integral of x+e^{2x}

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(e^{9x+5y})

\frac{\partial}{\partial x} (e^{9 x + 5 y})

derivative of (2x^2+1/((1-x^2)^{5/2)})

\frac{d}{d x} (\frac{2 x ^{2} + 1}{( 1 - x ^{2} ) ^{\frac{5}{2}}})

integral of 1/(2*sqrt(tan(x)))

\int \frac{1}{2 \cdot tan ( x )} d x

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

derivative of (1/(x^2-9/(x^4))(x+5x^3))

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) (x + 5 x^{3}))

Frequently Asked Questions (FAQ)

What is the integral of x+e^{2x} ?
The integral of x+e^{2x} is (x^2)/2+1/2 e^{2x}+C