What is the integral of e^{x/n} ?

The integral of e^{x/n} is ne^{x/n}+C

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integral of e^{x/n}

\int e^{\frac{x}{n}} d x

n e^{\frac{x}{n}} + C

Solution steps

\int e^{\frac{x}{n}} d x

Apply u-substitution

: \int e^{u} n d u

= \int e^{u} n d u

Take the constant out:

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

= n \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= n e^{u}

Substitute back

u = \frac{x}{n}

= n e^{\frac{x}{n}}

Add a constant to the solution

= n e^{\frac{x}{n}} + C

f (x) = \frac{1}{( 3 x ^{2} - 1 ) ^{2}}

f (x) = x^{2} + 3, (3, 12)

\int (3 x^{2} tan (y) - \frac{2 y ^{3}}{x ^{3}}) d x

f (x) = 3 csc (4 x)

(y^{4} - x^{2}) d y + x y d x = 0