What is the integral of e^{sin(pi)x}cos(pi)x ?

The integral of e^{sin(pi)x}cos(pi)x is -(x^2)/2+C

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integral of e^{sin(pi)x}cos(pi)x

\int e^{s i n (π) x} cos (π) x d x

- \frac{x ^{2}}{2} + C

Solution steps

\int e^{s i n (π) x} cos (π) x d x

Take the constant out:

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

= cos (π) \cdot \int e^{s i n (π) x} x d x

cos (π) = - 1

= (- 1) \cdot \int e^{s i n (π) x} x d x

Simplify

e^{s i n (π) x} x : x

= (- 1) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= (- 1) \frac{x ^{2}}{2}

Simplify

= - \frac{x ^{2}}{2}

Add a constant to the solution

= - \frac{x ^{2}}{2} + C

x \to 1 lim (x^{2} - 2 x - 1)

\int \frac{cos ( x )}{4 + sin ^{2} ( x )} d x

\int \frac{432}{w ^{2} 144 - w ^{2}} d w

f (x) = e^{3 x^{2}}

\int x tan^{2} (x) d x

What is the integral of e^{sin(pi)x}cos(pi)x ?
The integral of e^{sin(pi)x}cos(pi)x is -(x^2)/2+C