Question

$A:\int {\tan }^{4}x{\sec }^{2}xdx=\frac{1}{5}{\tan }^{5}x+c$
$R:\int \left[f\right(x\left){]}^n{f}^{\prime }\right(x)dx=\frac{\left[f\right(x){]}^{n+1}}{n+1}+c$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not correct explanation of A
• C. A is true R is false
• D. A is false but R is true.

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

$A=\int {\tan }^{4}x{\sec }^{2}xdx=\int {\tan }^{4}xd\left(\tan x\right)$
$=\frac{{\tan }^{5}x}{5}+c$
A: true
$B=\int \left[f\right(x){]}^n\cdot f^1(x)dx=\int [f\left(x\right){]}^{n}d\cdot f\left(x\right)$

$=\frac{f(x{)}^{n+1}}{n+1}+c$
R: correct
and R is correct explanation for A.