What is the integral from 0 to 1 of 162e^{2x}+324 ?

The integral from 0 to 1 of 162e^{2x}+324 is 81e^2+243

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integral from 0 to 1 of 162e^{2x}+324

\int_{0}^{1} 162 e^{2 x} + 324 d x

81 e^{2} + 243

Decimal

841.51354 \dots

Solution steps

\int_{0}^{1} 162 e^{2 x} + 324 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_{0}^{1} 162 e^{2 x} d x + \int_{0}^{1} 324 d x

\int_{0}^{1} 162 e^{2 x} d x = 81 (e^{2} - 1)

\int_{0}^{1} 324 d x = 324

= 81 (e^{2} - 1) + 324

Simplify

81 (e^{2} - 1) + 324 : 81 e^{2} + 243

= 81 e^{2} + 243

\int \frac{ln ^{3} ( x )}{x} d x

\frac{d}{d x} (2 x y + y^{2})

y = x - x^{2}, (- 1, - 2)

t^{3} sin (3 t)

f^{^{'}} (x) = 5 x + 1

What is the integral from 0 to 1 of 162e^{2x}+324 ?
The integral from 0 to 1 of 162e^{2x}+324 is 81e^2+243