Antiderivative of Trigonometric Functions

In calculus, a function F is said to be antiderivative of the function f if the derivative F' = f. The process of finding antiderivatives is called as antidifferentiation.

F(x) = int f(x) dx

Learning antiderivative of trigonometric functions from the tutor is interactive and fun than a book. Students feel more convenience to study antiderivative of trigonometric functions from the tutor.. Tutors conduct the regular tests to improve the student's knowledge about antiderivatives. Following is the list of antiderivatives formulas and example problems to show how the tutor helps to learn antiderivative of trigonometric functions.

Study antiderivative formulas for trigonometric functions from tutor:

int sin x dx = - cos x + C

int cos x dx = sin x + C

int sec2 x dx = tan x + C

int cosec2 x dx = - cot x + C

int sec x tan x dx = sec x + C

int cosec x cot x dx = - cosec x + C

int tan x dx = ln |sec x| + C

int cot x dx = - ln |cosec x| + C

int sec x dx = ln |sec x + tan x| + C

int cosec x dx = ln |cosec x - cot x| + C

Study antiderivative of trigonometric functions with example problems from tutor:

Example problem 1:

Find antiderivative of a function,  f(x) = 7cos (5x)

Solution:

Step 1: Given function

f(x) =7cos (5x)

int f(x) dx = int 7cos (5x) dx

Step 2: Integrate the given function with respect to ' x',

int7cos (5x) dx = 7(sin (5x)) 1/5

= (7sin (5x))/5

Example problem 2:

Find antiderivative of a function y = 5sec2 (9x)

Solution:

Step 1: Given function

y = 5sec2 9x

int y dx = int 5sec2 9x dx

Step 2: Integrate the given function y = 5sec2 9x with respect to ' x',

int5sec2 9x dx = 5tan (9x) 1/9

= (5tan (9x))/9

Example problem 3:

Find antiderivative of a function, f(x) = 5sin (4x) + sec (6x)

Solution:

Step 1: Given function

f(x) = 5sin (4x) + sec (6x)

int f(x) dx = int 5sin (4x) + sec (6x)dx

Step 2: Separate the integral function

int 5sin (4x) + sec (6x) dx = int  5sin (4x) dx + int sec (6x) dx

Step 2: Integrate the above function with respect to ' x ',

int5sin (4x) + sec (6x) dx = (-5cos (4x))/4 + (log (sec (6x) + tan (6x)))/6 + C