Consider I=∫cos^3 x dx I=∫cos 3x+3cos x4 dx #160; #160; #160; [∵ cos3A=( 4cos ^ 3 A 3cos A )] #160; I=14∫cos 3x +3cos x dx ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

Integrate ∫...

Question

Integrate $\int {cos}^{3} x d x$

Open in App

Solution

Consider $I = \int {cos}^{3} x d x$

$I = \int \frac{cos 3 x + 3 cos x}{4} d x$ $[∵ c o s 3 A = (4 {cos}^{3} A - 3 cos A)]$

$I = \frac{1}{4} \int cos 3 x + 3 cos x d x$

$I = \frac{1}{4} \int cos 3 x d x + \frac{1}{4} \int 3 cos x d x$

$I = \frac{1}{4} [\frac{sin 3 x}{3} + 3 sin x] + C$

Suggest Corrections

Similar questions

Q. Integrate:

\int {cos}^{3} x d x

\int e^{{sin}^{2} x} sin x (cos x + {cos}^{3} x) d x

is equal to
(where

C

is constant of integration)

\int \cos^{3} \sqrt{x} d x

Given $\int sin (x) d x = - cos (x)$ and $\int cos (x) d x = sin (x)$ . If $f (x) = 36 \int (sin (2 x) + cos (3 x)] d x$ , then find the value of $- f (π)$ [ take constant of integration equal to zero]

___

\int \frac{1}{1 + \cos 3 x} d x

Join BYJU'S Learning Program

Integrate ∫cos3x dx

Consider I=∫cos3x dxI=∫cos3x+3cosx4 dx [∵cos3A=(4cos3A−3cosA)] I=14∫cos3x+3cosx dxI=14∫cos3x dx+14∫3cosx dxI=14[sin3x3+3sinx]+C

Integrate $\int {cos}^{3} x d x$

Consider $I = \int {cos}^{3} x d x$

$I = \int \frac{cos 3 x + 3 cos x}{4} d x$ $[∵ c o s 3 A = (4 {cos}^{3} A - 3 cos A)]$

$I = \frac{1}{4} \int cos 3 x + 3 cos x d x$

$I = \frac{1}{4} \int cos 3 x d x + \frac{1}{4} \int 3 cos x d x$

$I = \frac{1}{4} [\frac{sin 3 x}{3} + 3 sin x] + C$