How do you find the antiderivative of #f(x) = 1 / (5cos^2(5x))#?

Answer 1

Elijah Abram

#tan(5x)/25 + C#

As the derivative of #tan(x)# is #1/cos^2(x)#, we can deduce that #int1/(5cos^2(5x))=tan(5x)/25+ "Constant"#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ezekiel Alexander

To find the antiderivative of ( f(x) = \frac{1}{5\cos^2(5x)} ), you can use the trigonometric identity ( \cos^2(x) = \frac{1}{2}(1 + \cos(2x)) ). Then, rewrite the function in terms of this identity, integrate term by term, and apply the appropriate antiderivative rules. The antiderivative involves the arctangent function. The antiderivative of ( f(x) ) is:

[ F(x) = \frac{1}{5} \tan(5x) + C ]

where ( C ) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.