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Popular >

integral of-3/(e^t)

Solution

\int - \frac{3}{e ^{t}} d t

Solution

\frac{3}{e ^{t}} + C

Solution steps

\int - \frac{3}{e ^{t}} d t

Take the constant out:

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

= - 3 \cdot \int \frac{1}{e ^{t}} d t

Apply u-substitution

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

= - 3 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 3 (- \frac{1}{u})

Substitute back

u = e^{t}

= - 3 (- \frac{1}{e ^{t}})

Simplify

- 3 (- \frac{1}{e ^{t}}) : \frac{3}{e ^{t}}

= \frac{3}{e ^{t}}

Add a constant to the solution

= \frac{3}{e ^{t}} + C

Graph

Popular Examples

integral of x^2(7x^3-9)^5

\int x^{2} (7 x^{3} - 9)^{5} d x

integral of (sqrt(1-x))/(1+x)

\int \frac{1 - x}{1 + x} d x

integral of t/(t^2+4)

\int \frac{t}{t ^{2} + 4} d t

integral of (3x^2-5x+2)

\int (3 x^{2} - 5 x + 2) d x

integral of 5^{3x^2}

\int 5^{3 x^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of-3/(e^t) ?
The integral of-3/(e^t) is 3/(e^t)+C