What is the integral of e^{2x+1} ?

The integral of e^{2x+1} is 1/2 e^{2x+1}+C

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integral of e^{2x+1}

\int e^{2 x + 1} d x

\frac{1}{2} e^{2 x + 1} + C

Solution steps

\int e^{2 x + 1} d x

Apply u-substitution

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

= \int e^{u} \frac{1}{2} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = 2 x + 1

= \frac{1}{2} e^{2 x + 1}

Add a constant to the solution

= \frac{1}{2} e^{2 x + 1} + C

x \to 3 + lim (\frac{- x}{x - 3})

x \to 8 lim (\frac{3}{( x - 8 ) ^{2}})

\int 13 tan^{4} (x) sec^{6} (x) d x

\frac{6 x}{x + 5}

f (x) = 2 x^{2} - 6 x + 4