What is the integral from 0 to pi of 5e^x+3sin(x) ?

The integral from 0 to pi of 5e^x+3sin(x) is 5e^pi+1

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integral from 0 to pi of 5e^x+3sin(x)

\int_{0}^{π} 5 e^{x} + 3 sin (x) d x

5 e^{π} + 1

Decimal

116.70346 \dots

Solution steps

\int_{0}^{π} 5 e^{x} + 3 sin (x) 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}^{π} 5 e^{x} d x + \int_{0}^{π} 3 sin (x) d x

\int_{0}^{π} 5 e^{x} d x = 5 (e^{π} - 1)

\int_{0}^{π} 3 sin (x) d x = 6

= 5 (e^{π} - 1) + 6

Simplify

5 (e^{π} - 1) + 6 : 5 e^{π} + 1

= 5 e^{π} + 1

\int_{0}^{\frac{π}{2}} 3 sin (x) d x

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\int_{0}^{1} x \cdot 3 x^{2} d x

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

What is the integral from 0 to pi of 5e^x+3sin(x) ?
The integral from 0 to pi of 5e^x+3sin(x) is 5e^pi+1