What is the integral from-ln(4) to 0 of 3sqrt(3)e^t ?

The integral from-ln(4) to 0 of 3sqrt(3)e^t is (9sqrt(3))/4

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integral from-ln(4) to 0 of 3sqrt(3)e^t

\int_{- l n (4)}^{0} 33 e^{t} d t

\frac{9 3}{4}

Solution steps

\int_{- l n (4)}^{0} 33 e^{t} d t

Take the constant out:

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

= 33 \cdot \int_{- l n (4)}^{0} e^{t} d t

Use the common integral:

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

= 33 [e^{t}]_{- l n (4)}^{0}

Simplify

ln (4) : 2 ln (2)

= 33 [e^{t}]_{- 2 l n (2)}^{0}

Compute the boundaries:

\frac{3}{4}

= 33 \frac{3}{4}

Simplify

= \frac{9 3}{4}

\frac{1}{6 x ^{2} + 5}

\int 15 x^{29} cos (x^{15}) d x

\frac{d ^{2}}{d x ^{2}} (cos (3 x))

\frac{d}{d x} (ln (1 - ln (x)))

1 + e^{2 x}

What is the integral from-ln(4) to 0 of 3sqrt(3)e^t ?
The integral from-ln(4) to 0 of 3sqrt(3)e^t is (9sqrt(3))/4