What is the integral of sin(3/4)xcos^2(3/4)x ?

The integral of sin(3/4)xcos^2(3/4)x is (cos^2(3/4))/3 sin(3/4)x^3+C

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integral of sin(3/4)xcos^2(3/4)x

\int sin (\frac{3}{4}) x cos^{2} (\frac{3}{4}) x d x

\frac{cos ^{2} ( \frac{3}{4} )}{3} sin (\frac{3}{4}) x^{3} + C

Solution steps

\int sin (\frac{3}{4}) x cos^{2} (\frac{3}{4}) x d x

Take the constant out:

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

= sin (\frac{3}{4}) cos^{2} (\frac{3}{4}) \cdot \int xx d x

Simplify

xx : x^{2}

= sin (\frac{3}{4}) cos^{2} (\frac{3}{4}) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= sin (\frac{3}{4}) cos^{2} (\frac{3}{4}) \frac{x ^{3}}{3}

Simplify

sin (\frac{3}{4}) cos^{2} (\frac{3}{4}) \frac{x ^{3}}{3} : \frac{cos ^{2} ( \frac{3}{4} )}{3} sin (\frac{3}{4}) x^{3}

= \frac{cos ^{2} ( \frac{3}{4} )}{3} sin (\frac{3}{4}) x^{3}

Add a constant to the solution

= \frac{cos ^{2} ( \frac{3}{4} )}{3} sin (\frac{3}{4}) x^{3} + C

n = 1 (1 - \frac{1}{n}) \sum \infty n^{2}

\int_{2}^{4} (2 x - 3) (3 x + 1) d x

\frac{1}{y ^{2}} \cdot (y \cdot x + x^{2})

\int 2 r^{2} d r

x cos (1 - e^{x})

What is the integral of sin(3/4)xcos^2(3/4)x ?
The integral of sin(3/4)xcos^2(3/4)x is (cos^2(3/4))/3 sin(3/4)x^3+C