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 Notation

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

\frac{\partial}{\partial x} (3 t sin^{2} (t))

f (x) = 5 x - 1

x^{4} y^{^{'}} + 3 x^{3} y = x^{2} e^{x}

\frac{d}{d x} (\frac{3 x - 9}{2 x + 4})

\int \frac{1}{16 x ^{2} + 25} 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