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

The integral of e^{ln(2t)} is t^2+C

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integral of e^{ln(2t)}

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

t^{2} + C

Solution steps

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

Apply log rule:

a^{l o g_{a} (b)} = b

= \int 2 t d t

Take the constant out:

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

= 2 \cdot \int t d t

Apply the Power Rule

: \frac{t ^{2}}{2}

= 2 \cdot \frac{t ^{2}}{2}

Simplify

2 \cdot \frac{t ^{2}}{2} : t^{2}

= t^{2}

Add a constant to the solution

= t^{2} + C

\frac{1}{( s + 1 ) ^{2} ( s + 2 )}

- \frac{5}{2} x^{2} + 2 x + 2

\int 3 x^{2} y^{2} d x

\int_{3}^{5} (x^{4} - \frac{3}{x ^{3}}) d x

2 (ln (y)) y^{^{'}} - x^{5} y = 0