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Popular >

integral of 1-e^{2t}

Solution

\int 1 - e^{2 t} d t

Solution

t - \frac{1}{2} e^{2 t} + C

Solution steps

\int 1 - e^{2 t} d t

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 t - \int e^{2 t} d t

\int 1 d t = t

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

= t - \frac{1}{2} e^{2 t}

Add a constant to the solution

= t - \frac{1}{2} e^{2 t} + C

Popular Examples

integral of (tan(x)+1)^{-1}

\int (tan (x) + 1)^{- 1} d x

integral of (3x)/((x^2-1))

\int \frac{3 x}{( x ^{2} - 1 )} d x

integral of 1rctan(x)

\int 1 d arctan (x) d x

integral of sqrt(x^2(a^2-x^2))

\int x^{2} (a^{2} - x^{2}) d x

integral of 2x^2-x+1

\int 2 x^{2} - x + 1 d x

Frequently Asked Questions (FAQ)

What is the integral of 1-e^{2t} ?
The integral of 1-e^{2t} is t-1/2 e^{2t}+C