What is the integral of A*e^{t(1+sqrt(3))} ?

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

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integral of A*e^{t(1+sqrt(3))}

\int A \cdot e^{t (1 + 3)} d t

A \frac{3 - 1}{2} e^{t (1 + 3)} + C

Solution steps

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

Take the constant out:

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

= A \cdot \int e^{t (1 + 3)} d t

Apply u-substitution

: \int \frac{3 - 1}{2} e^{u} d u

= A \cdot \int \frac{3 - 1}{2} e^{u} d u

Take the constant out:

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

= A \frac{3 - 1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= A \frac{3 - 1}{2} e^{u}

Substitute back

u = t (1 + 3)

= A \frac{3 - 1}{2} e^{t (1 + 3)}

Add a constant to the solution

= A \frac{3 - 1}{2} e^{t (1 + 3)} + C

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