Advertisements
Advertisements
Question
\[\int \sin^4 x \cos^3 x \text{ dx }\]
Sum
Solution
∫ 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
\[= \frac{t^5}{5} - \frac{t^7}{7} + C\]
\[ = \frac{\sin^5 x}{5} - \frac{\sin^7 x}{7} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\sqrt{x}\left( 3 - 5x \right) dx\]
\[\int\frac{1 - \cos 2x}{1 + \cos 2x} dx\]
\[\int\frac{\cos x}{1 - \cos x} \text{dx }or \int\frac{\cot x}{\text{cosec } {x }- \cot x} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]
\[\int\frac{\sec^2 x}{\tan x + 2} dx\]
\[\int\frac{\sin 2x}{\sin 5x \sin 3x} dx\]
` ∫ x {tan^{- 1} x^2}/{1 + x^4} dx`
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int \cos^5 x \text{ dx }\]
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{1}{\sqrt{3 x^2 + 5x + 7}} dx\]
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} dx\]
\[\int\frac{x^3 + x^2 + 2x + 1}{x^2 - x + 1}\text{ dx }\]
\[\int\frac{1}{3 + 2 \sin x + \cos x} \text{ dx }\]
\[\int\frac{1}{p + q \tan x} \text{ dx }\]
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
\[\int {cosec}^3 x\ dx\]
\[\int\frac{\sin^{- 1} x}{x^2} \text{ dx }\]
\[\int e^x \left( \cot x - {cosec}^2 x \right) dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int\sqrt{2x - x^2} \text{ dx}\]
\[\int\frac{x^3}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{x^2}{\left( x^2 + 1 \right) \left( 3 x^2 + 4 \right)} dx\]
\[\int\frac{\sin x}{3 + 4 \cos^2 x} dx\]
\[\int e^x \left( \frac{1 - \sin x}{1 - \cos x} \right) dx\]
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int \cos^5 x\ dx\]
\[\int\frac{\sin 2x}{\sin^4 x + \cos^4 x} \text{ dx }\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int x\sqrt{1 + x - x^2}\text{ dx }\]
\[\int x^2 \tan^{- 1} x\ dx\]
\[\int \sec^{- 1} \sqrt{x}\ dx\]
\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
\[\int\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} \text{ dx}\]
