SOLVED: Find ∫sin 5x cos 4x dx.

Trigonometric Integrals
Trigonometric Integrals

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Hi in the given problem, we are required to solve the integral of sin to the power 5 x times cos to the power 4 x dx. So here we’ll be taking the you will be using the substitution method where we’ll take? U as cos of x. Now, when we differentiate this, we have d: u is equal to minus sine x, dx, so in place of d. U i can write minus sine x d x, so here this integral, i is equal to integration. Now this can be written as sine to the power 4 x times sine x times, cos to the power 4 x d x. Now, after a substitution, this is integration of 1 minus cos square x, whole square because sine square you know sine squared x is equal to 1 minus cos square x. So if we take the square of this, we have to take the square of that. So this is sin to the power 4 x, which is 1 minus cos square x, whole square. So from this we get this now times cos 4 x cos the power 4 x times sine x d x. Now sine…

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