What is the integral of-(4000)/((1+0.4t)^2) ?

The integral of-(4000)/((1+0.4t)^2) is (10000)/(1+0.4t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-(4000)/((1+0.4t)^2)

\int - \frac{4000}{( 1 + 0.4 t ) ^{2}} d t

\frac{10000}{1 + 0.4 t} + C

Solution steps

\int - \frac{4000}{( 1 + 0.4 t ) ^{2}} d t

Take the constant out:

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

= - 4000 \cdot \int \frac{1}{( 1 + 0.4 t ) ^{2}} d t

Apply u-substitution

: \int \frac{1}{0.4 u ^{2}} d u

= - 4000 \cdot \int \frac{1}{0.4 u ^{2}} d u

Take the constant out:

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

= - 4000 \cdot \frac{1}{0.4} \cdot \int \frac{1}{u ^{2}} d u

Simplify

= - 4000 \cdot 2.5 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 4000 \cdot 2.5 (- \frac{1}{u})

Substitute back

u = 1 + 0.4 t

= - 4000 \cdot 2.5 (- \frac{1}{1 + 0.4 t})

Simplify

- 4000 \cdot 2.5 (- \frac{1}{1 + 0.4 t}) : \frac{10000}{1 + 0.4 t}

= \frac{10000}{1 + 0.4 t}

Add a constant to the solution

= \frac{10000}{1 + 0.4 t} + C

\int x^{\frac{1}{4}} + 8 d x

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

\int \frac{1}{8 t} d t

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

\int \frac{0.4 x ^{3}}{0.2 x ^{4} + 8000} d x

What is the integral of-(4000)/((1+0.4t)^2) ?
The integral of-(4000)/((1+0.4t)^2) is (10000)/(1+0.4t)+C