What is the integral of (e^t)/((1+e^{(2t)))^{(3/2)}} ?

The integral of (e^t)/((1+e^{(2t)))^{(3/2)}} is (e^t)/((1+e^{2t))^{1/2}}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^t)/((1+e^{(2t)))^{(3/2)}}

\int \frac{e ^{t}}{( 1 + e ^{(2 t)} ) ^{(\frac{3}{2})}} d t

\frac{e ^{t}}{( 1 + e ^{2 t} ) ^{\frac{1}{2}}} + C

Solution steps

\int \frac{e ^{t}}{( 1 + e ^{2 t} ) ^{\frac{3}{2}}} d t

Apply u-substitution

: \int \frac{1}{( 1 + u ^{2} ) ^{\frac{3}{2}}} d u

= \int \frac{1}{( 1 + u ^{2} ) ^{\frac{3}{2}}} d u

Apply Trigonometric Substitution

: \int cos (v) d v

= \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= sin (v)

Substitute back

= sin (arctan (e^{t}))

Simplify

sin (arctan (e^{t})) : \frac{e ^{t}}{( 1 + e ^{2 t} ) ^{\frac{1}{2}}}

= \frac{e ^{t}}{( 1 + e ^{2 t} ) ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{e ^{t}}{( 1 + e ^{2 t} ) ^{\frac{1}{2}}} + C

\int 3 x - 2 d x

\frac{d y}{d x} = 3 y \cdot e^{x + 3}

y = \frac{x ^{2} + 7}{5 x - x ^{2}}, 1, 4

\frac{\partial}{\partial x} (r sin (x))

y^{^{'}} = 1

What is the integral of (e^t)/((1+e^{(2t)))^{(3/2)}} ?
The integral of (e^t)/((1+e^{(2t)))^{(3/2)}} is (e^t)/((1+e^{2t))^{1/2}}+C