What is the integral of sin(x)in(cos(x)) ?

The integral of sin(x)in(cos(x)) is (in)/2 sin^2(x)+C

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integral of sin(x)in(cos(x))

\int sin (x) in (cos (x)) d x

\frac{in}{2} sin^{2} (x) + C

Solution steps

\int sin (x) in cos (x) d x

Take the constant out:

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

= in \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= in \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= in \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= in \frac{sin ^{2} ( x )}{2}

Simplify

in \frac{sin ^{2} ( x )}{2} : \frac{in}{2} sin^{2} (x)

= \frac{in}{2} sin^{2} (x)

Add a constant to the solution

= \frac{in}{2} sin^{2} (x) + C

f (x) = 8 sec (x) tan (x)

f (x) = x^{2} + 1, (0, 1)

n = 5 \sum \infty \frac{3 ^{n}}{1 2 ^{n}}

y = x^{2} - 5

x \to - 1 lim (4 x^{2} - 2 x - 6)

What is the integral of sin(x)in(cos(x)) ?
The integral of sin(x)in(cos(x)) is (in)/2 sin^2(x)+C