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Popular >

integral of-1/(e^t)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = e^{t}

= - (- \frac{1}{e ^{t}})

Simplify

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

Add a constant to the solution

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

Popular Examples

integral of 4x^2e^{6x}

\int 4 x^{2} e^{6 x} d x

integral of (1+tan^2(x))/(sec^2(x))-1

\int \frac{1 + tan ^{2} ( x )}{sec ^{2} ( x )} - 1 d x

integral of x^{sqrt(a)}+1/(x^b)+c^3

\int x^{a} + \frac{1}{x ^{b}} + c^{3} d x

integral of 13sin^{-3/2}(x)cos^3(x)

\int 13 sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

integral of 8+2x-x^2

\int 8 + 2 x - x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of-1/(e^t) ?
The integral of-1/(e^t) is 1/(e^t)+C