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Popular >

integral of 2x-3e^x

Solution

\int 2 x - 3 e^{x} d x

Solution

x^{2} - 3 e^{x} + C

Solution steps

\int 2 x - 3 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 3 e^{x} d x

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

\int 3 e^{x} d x = 3 e^{x}

= x^{2} - 3 e^{x}

Add a constant to the solution

= x^{2} - 3 e^{x} + C

Popular Examples

derivative of 2x^2+5x+18

\frac{d}{d x} (2 x^{2} + 5 x + 18)

limit as t approaches 0 of (8^t-5^t)/t

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

integral of (y^2)/(y+1)

\int \frac{y ^{2}}{y + 1} d y

(\partial)/(\partial u)(vsin(u))

\frac{\partial}{\partial u} (v sin (u))

derivative of sqrt(2)sec(x)

\frac{d}{d x} (2 sec (x))

Frequently Asked Questions (FAQ)

What is the integral of 2x-3e^x ?
The integral of 2x-3e^x is x^2-3e^x+C