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प्रश्न
\[\int \sin^4 x \cos^3 x \text{ dx }\]
योग
उत्तर
∫ sin4 x cos3 x dx
= ∫ sin4 x . cos2 x cos x dx
= ∫ sin4 x . (1 – sin2 x ) cos x dx
Let sin x = t
⇒ cos x dx = dt
Now, ∫ sin4 x . (1 – sin2 x ) cos x dx
= ∫ t4 (1 – t2) dt
= ∫ (t4 – t6) dt
\[= \frac{t^5}{5} - \frac{t^7}{7} + C\]
\[ = \frac{\sin^5 x}{5} - \frac{\sin^7 x}{7} + C\]
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