What is the integral of asin(x)cos(x) ?

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

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integral of asin(x)cos(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= a \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Simplify

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

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

Add a constant to the solution

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

\int 3 cos (x) sin^{2} (x) d x

\int \frac{1}{( 4 x ^{2} - 9 ) ^{3}} d x

\int - t cos (2 t) d t

\int 2 x^{3} - 5 x^{2} - 3 x + 4 d x

\int \frac{x + 1}{4 x ^{2} - x} d x

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