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Popular >

integral of 4-e^{-x}

Solution

\int 4 - e^{- x} d x

Solution

4 x + e^{- x} + C

Solution steps

\int 4 - e^{- x} d x

Apply u-substitution

: \int - 4 + e^{u} d u

= \int - 4 + e^{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 4 d u + \int e^{u} d u

\int 4 d u = 4 u

\int e^{u} d u = e^{u}

= - 4 u + e^{u}

Substitute back

u = - x

= - 4 (- x) + e^{- x}

Simplify

= 4 x + e^{- x}

Add a constant to the solution

= 4 x + e^{- x} + C

Popular Examples

integral of (cos(u))/(sin^2(u))

\int \frac{cos ( u )}{sin ^{2} ( u )} d u

integral of x/(sqrt(1-9x^4))

\int \frac{x}{1 - 9 x ^{4}} d x

integral of (8x-1)/(x^2+x-6)

\int \frac{8 x - 1}{x ^{2} + x - 6} d x

integral of (x-2)/(x^2-4x+1)

\int \frac{x - 2}{x ^{2} - 4 x + 1} d x

integral of ((3x+7))/((x+5)(x+1))

\int \frac{( 3 x + 7 )}{( x + 5 ) ( x + 1 )} d x

Frequently Asked Questions (FAQ)

What is the integral of 4-e^{-x} ?
The integral of 4-e^{-x} is 4x+e^{-x}+C