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Popular >

integral of 5/(e^t)

Solution

\int \frac{5}{e ^{t}} d t

Solution

- \frac{5}{e ^{t}} + C

Solution steps

\int \frac{5}{e ^{t}} d t

Take the constant out:

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

= 5 \cdot \int \frac{1}{e ^{t}} d t

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 5 (- \frac{1}{u})

Substitute back

u = e^{t}

= 5 (- \frac{1}{e ^{t}})

Simplify

5 (- \frac{1}{e ^{t}}) : - \frac{5}{e ^{t}}

= - \frac{5}{e ^{t}}

Add a constant to the solution

= - \frac{5}{e ^{t}} + C

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\int \frac{1}{( 9 x ^{2} + 64 ) ^{2}} d x

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\int \frac{1}{x ^{2} + 144} d x

Frequently Asked Questions (FAQ)

What is the integral of 5/(e^t) ?
The integral of 5/(e^t) is -5/(e^t)+C