What is the integral from-4 to ln(3/4) of 4e^x-3 ?

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

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integral from-4 to ln(3/4) of 4e^x-3

\int_{- 4}^{l n (\frac{3}{4})} 4 e^{x} - 3 d x

- 9 - 3 ln (\frac{3}{4}) - \frac{4}{e ^{4}}

Decimal

- 8.21021 \dots

Solution steps

\int_{- 4}^{l n (\frac{3}{4})} 4 e^{x} - 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 4}^{l n (\frac{3}{4})} 4 e^{x} d x - \int_{- 4}^{l n (\frac{3}{4})} 3 d x

\int_{- 4}^{l n (\frac{3}{4})} 4 e^{x} d x = 3 - \frac{4}{e ^{4}}

\int_{- 4}^{l n (\frac{3}{4})} 3 d x = 3 ln (\frac{3}{4}) + 12

= 3 - \frac{4}{e ^{4}} - (3 ln (\frac{3}{4}) + 12)

Simplify

= - 9 - 3 ln (\frac{3}{4}) - \frac{4}{e ^{4}}

\int_{0}^{3} \frac{1}{x + 4} d x

\int_{1}^{4} \frac{k}{x} d x

\int_{1}^{3} \frac{1}{x ^{5}} d x

\int_{0}^{4 - y^{2} - z^{2}} 1 d x

\int_{5}^{7} \frac{1}{x - 2} d x

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