# What is the Integral of #tan^5(x) dx#?

Solution:

God bless....I hope the explanation is useful.

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

The integral of tan^5(x) dx is:

∫tan^5(x) dx = ∫tan(x) * tan^4(x) dx = ∫tan(x) * (sec^2(x) - 1)^2 * tan^2(x) dx

Letting u = tan(x), du = sec^2(x) dx, the integral becomes:

= ∫(u)(u^2 - 1)^2 du

Expanding and integrating:

= ∫(u^5 - 2u^3 + u) du = (1/6)u^6 - (1/2)u^4 + (1/2)u^2 + C

Substituting back u = tan(x):

= (1/6)tan^6(x) - (1/2)tan^4(x) + (1/2)tan^2(x) + C

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

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.

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.

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.

- How do you find the sum of the finite geometric sequence of #sum_(j=1)^6 32(1/4)^(j-1)# ?
- How do you evaluate the indefinite integral #int (2x^2-4x+3)dx#?
- How do you find the definite integral for: #e^sin(x) * cos(x) dx# for the intervals #[0, pi/4]#?
- What is the integral of #e^(2x)#?
- What is #int ln(x)^2+xdx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7