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Popular >

integral of 2x+5e^x

Solution

\int 2 x + 5 e^{x} d x

Solution

x^{2} + 5 e^{x} + C

Solution steps

\int 2 x + 5 e^{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 2 x d x + \int 5 e^{x} d x

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

\int 5 e^{x} d x = 5 e^{x}

= x^{2} + 5 e^{x}

Add a constant to the solution

= x^{2} + 5 e^{x} + C

Popular Examples

derivative of 8x-1

\frac{d}{d x} (8 x - 1)

y^{''}+9y=0,y(0)=5,y^'(0)=1

y^{^{''}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 1

limit as x approaches 9 of (7x)/(x-9)

x \to 9 lim (\frac{7 x}{x - 9})

integral of sec^2(3x+2)

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

integral of (2x-4)/(x^2-x)

\int \frac{2 x - 4}{x ^{2} - x} d x

Frequently Asked Questions (FAQ)

What is the integral of 2x+5e^x ?
The integral of 2x+5e^x is x^2+5e^x+C