Advertisements
Advertisements
Question
\[\int \sin^5 x \cos x \text{ dx }\]
Sum
Advertisements
Solution
∫ sin5 x cos x dx
Let sin x = t
cos x dx = dt
Now, ∫ sin5 x cos x dx
= ∫ t5 . dt
\[= \frac{t^6}{6} + C\]
\[ = \frac{\sin^6 x}{6} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
If f' (x) = 8x3 − 2x, f(2) = 8, find f(x)
\[\int\frac{2x + 3}{\left( x - 1 \right)^2} dx\]
\[\int\frac{3x + 5}{\sqrt{7x + 9}} dx\]
\[\int\left( 5x + 3 \right) \sqrt{2x - 1} dx\]
Integrate the following integrals:
\[\int\text { sin x cos 2x sin 3x dx}\]
\[\int\sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} dx\]
\[\int\frac{\cos x - \sin x}{1 + \sin 2x} dx\]
\[\int\frac{\cos\sqrt{x}}{\sqrt{x}} dx\]
\[\int\frac{x^2}{\sqrt{1 - x}} dx\]
` ∫ tan^5 x sec ^4 x dx `
` ∫ \sqrt{tan x} sec^4 x dx `
\[\int \sec^4 2x \text{ dx }\]
\[\int\frac{x^4 + 1}{x^2 + 1} dx\]
\[\int\frac{1}{x^2 - 10x + 34} dx\]
\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
` ∫ { x^2 dx}/{x^6 - a^6} dx `
\[\int\frac{1}{\sqrt{5 x^2 - 2x}} dx\]
\[\int\frac{\left( x - 1 \right)^2}{x^2 + 2x + 2} dx\]
\[\int\frac{x + 1}{\sqrt{4 + 5x - x^2}} \text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{1}{3 + 2 \sin x + \cos x} \text{ dx }\]
`int 1/(sin x - sqrt3 cos x) dx`
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int \left( \log x \right)^2 \cdot x\ dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx }\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\frac{x^3}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{2x}{\left( x^2 + 1 \right) \left( x^2 + 3 \right)} dx\]
\[\int\frac{x}{\left( x^2 - a^2 \right) \left( x^2 - b^2 \right)} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{\left( x^2 + 1 \right) \left( x^2 + 2 \right)}{\left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{2x + 3}} \text{ dx }\]
\[\int \cot^5 x\ dx\]
\[\int \sec^4 x\ dx\]
\[\int\sqrt{a^2 - x^2}\text{ dx }\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
Evaluate : \[\int\frac{\cos 2x + 2 \sin^2 x}{\cos^2 x}dx\] .
