^3 2x ^5 2x dx =

MCQ

$\int {\frac{{{{\sin }^3}2x}}{{{{\cos }^5}2x}}dx = } $

A
${\tan ^4}x + C$
B
$\tan 4x + C$
C
${\tan ^4}2x + x + C$
✓
$\frac{1}{8}{\tan ^4}2x + C$

✓

Answer

Correct option: D.

$\frac{1}{8}{\tan ^4}2x + C$

d
(d) $I = \int {\frac{{{{\sin }^3}2x}}{{{{\cos }^5}2x}}dx} $
==> $I = \int {\frac{{{{\sin }^3}2x}}{{{{\cos }^3}2x}}.\frac{1}{{{{\cos }^2}2x}}dx = \int {{{\tan }^3}2x.{{\sec }^2}2x\,dx.} } $
Putting tan $2x = t$ and $2{\sec ^2}2x\,dx = dt$, we get
$I = \int {{t^3}\frac{{dt}}{2} = \frac{1}{2}.\frac{{{t^4}}}{4} + C = \frac{1}{8}({{\tan }^4}2x) + C.} $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The latus rectum of the conic passing through the origin and having the property that normal at each point $(x, y)$ intersects the $x -$ axis at $((x + 1), 0)$ is :

→

Let $\operatorname{Max} \limits _{0 \leq x \leq 2}\left\{\frac{9-x^{2}}{5-x}\right\}=\alpha$ and $\operatorname{Min} \limits _ {0 \leq x \leq 2}\left\{\frac{9-x^{2}}{5-x}\right\}=\beta$

If $\int\limits_{\beta-\frac{8}{3}}^{2 a-1} \operatorname{Max}\left\{\frac{9- x ^{2}}{5- x }, x \right\} dx =\alpha_{1}+\alpha_{2} \log _{e}\left(\frac{8}{15}\right)$ then $\alpha_{1}+\alpha_{2}$ is equal to

→

$\int_{}^{} {\frac{{2x{{\tan }^{ - 1}}{x^2}}}{{1 + {x^4}}}} \;dx = $

→

Let $G$ be the centroid of $\triangle{\text{ABC}}$. if $\overrightarrow{\text{AB}}=\vec{\text{a}},\overrightarrow{\text{AC}}=\vec{\text{b}}$, then the bisector $\overrightarrow{\text{AG}}$, in terms of $\vec{\text{a}}$ and $\vec{\text{b}}$ is,

→

The corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2 x+3 y$ is $.......$

→

If A and B are invertible matrices, then which of the following is not correct?

→

If the general solution of the differential equation $y' = \frac{y}{x} + \phi \left( {\frac{x}{y}} \right)$ , for some function $\phi $, is given by $y \ln \,\left| {cx} \right| = x$, where $c$ is an arbitrary constant, then $\phi \,(2)$ is equal to:

→

The possible number of different orders that a matrix can have when it has $24$ elements, is :