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intcos^(3)(x)sin(x)dx=

∫cos⁡3(x)sin⁡(x)dx= \int \cos ^{3}(x) \sin (x) d x=

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Evaluate definite integrals using the power ruleright chevron icon

Full solution

Q. ∫cos⁡3(x)sin⁡(x)dx= \int \cos ^{3}(x) \sin (x) d x=
  1. Rewrite in terms of uu: Rewrite the integral in terms of uu.∫cos⁡3(x)sin⁡(x) dx=∫u3(−du)=−∫u3 du\int \cos^3(x)\sin(x)\,dx = \int u^3(-du) = -\int u^3\,du
  2. Integrate u3u^3: Now, integrate u3u^3 with respect to uu.−∫u3 du=−u44+C-\int u^3\,du = -\frac{u^4}{4} + C
  3. Substitute back cos⁡(x)\cos(x): Substitute back cos⁡(x)\cos(x) for uu.\newline−u4/4+C=−cos⁡4(x)/4+C-u^4/4 + C = -\cos^4(x)/4 + C
  4. Correct integration mistake: We made a mistake in the integration step; the integral of u3u^3 should be u44\frac{u^4}{4}, not −u44-\frac{u^4}{4}.

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