What is the integral of e^{2x+ln(x)} ?

The integral of e^{2x+ln(x)} is 1/4 (e^{2x}*2x-e^{2x})+C

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integral of e^{2x+ln(x)}

\int e^{2 x + l n (x)} d x

\frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

Solution steps

\int e^{2 x + l n (x)} d x

Simplify

e^{2 x + l n (x)} : e^{2 x} x

= \int e^{2 x} x d x

Apply u-substitution

: \int \frac{e ^{u} u}{4} d u

= \int \frac{e ^{u} u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{4} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{4} (e^{u} u - e^{u})

Substitute back

u = 2 x

= \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

Add a constant to the solution

= \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

x \to 7 - lim (\frac{1}{x ^{2} ( x + 7 )})

\int \frac{2 x ^{3}}{2 x ^{2} - 4 x + 3} d x

\int x^{3} d x

\int 6 x e^{x^{2}} d x

P (t) = - 5 t^{2} + 75 t - 30

What is the integral of e^{2x+ln(x)} ?
The integral of e^{2x+ln(x)} is 1/4 (e^{2x}*2x-e^{2x})+C