What is the integral of $\int {sin}^{3} (x) {cos}^{3} (x) d x$ $int sin^3 (x)cos^3 (x) dx$ ?

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What is the integral of $\int {sin}^{3} (x) {cos}^{3} (x) d x$ $int sin^3 (x)cos^3 (x) dx$ ?

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Answer 1 · 2016-03-07T09:15:00

$\int {sin}^{3} x {cos}^{3} x d x = \frac{1}{4} {sin}^{4} x - \frac{1}{5} {sin}^{5} x + C$ $int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C$

Explanation:

$\int {sin}^{3} x {cos}^{3} x d x = ? sin x = u cos x d x = d u$ $int sin^3 x cos^3 x d x= ? " "sin x=u" "cos x d x=d u$
$\int {sin}^{3} x \cdot {cos}^{2} x \cdot cos x \cdot d x {cos}^{2} x = 1 - {sin}^{2} x$ $int sin^3 x* cos^2 x* cos x* d x" "cos^2 x=1-sin^2 x$
$\int u^{3} (1 - {sin}^{2}) d u \int u^{3} (1 - u^{2}) d u \int (u^{3} - u^{5}) d u$ $int u^3(1-sin^2)d u" "int u^3(1-u^2) d u" "int(u^3-u^5)d u$
$\int {sin}^{3} x {cos}^{3} x d x = \frac{1}{4} u^{4} - \frac{1}{5} u^{5} + C$ $int sin^3 x cos^3 x d x=1/4u^4-1/5u^5+C$
$\int {sin}^{3} x {cos}^{3} x d x = \frac{1}{4} {sin}^{4} x - \frac{1}{5} {sin}^{5} x + C$ $int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C$

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What is the integral of $\int {sin}^{3} (x) {cos}^{3} (x) d x$ $int sin^3 (x)cos^3 (x) dx$ ?

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What is the integral of $\int {sin}^{3} (x) {cos}^{3} (x) d x$ $int sin^3 (x)cos^3 (x) dx$ ?