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Popular >

integral of 1-e^{3x}

Solution

\int 1 - e^{3 x} d x

Solution

x - \frac{1}{3} e^{3 x} + C

Solution steps

\int 1 - e^{3 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 1 d x - \int e^{3 x} d x

\int 1 d x = x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= x - \frac{1}{3} e^{3 x}

Add a constant to the solution

= x - \frac{1}{3} e^{3 x} + C

Popular Examples

tangent of f(x)= 3/x ,(3,1)tangent of

f (x) = \frac{3}{x}, (3, 1)

x^2y^'+4xy=(sin(2x))/(x^2)

x^{2} y^{^{'}} + 4 x y = \frac{sin ( 2 x )}{x ^{2}}

derivative of Ce^{-x}

\frac{d}{d x} (C e^{- x})

integral of w/((1+w)^{3/4)}

\int \frac{w}{( 1 + w ) ^{\frac{3}{4}}} d w

y^{^{'}} = 6 x^{2} - 3 x^{2} y

Frequently Asked Questions (FAQ)

What is the integral of 1-e^{3x} ?
The integral of 1-e^{3x} is x-1/3 e^{3x}+C