Final answer to the problem
Step-by-step Solution
Specify the solving method
Apply the trigonometric identity: $\sin\left(x\right)\cos\left(y\right)$$=\frac{\sin\left(x+y\right)+\sin\left(x-y\right)}{2}$
Learn how to solve trigonometric integrals problems step by step online.
$\int\frac{\sin\left(9x\right)+\sin\left(x\right)}{2}dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(5x)cos(4x))dx. Apply the trigonometric identity: \sin\left(x\right)\cos\left(y\right)=\frac{\sin\left(x+y\right)+\sin\left(x-y\right)}{2}. Take the constant \frac{1}{2} out of the integral. Simplify the expression inside the integral. We can solve the integral \int\sin\left(x\right)dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution.