What is the integral of (sin^2(4x)+cos^2(4x)) ?

The integral of (sin^2(4x)+cos^2(4x)) is x+C

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integral of (sin^2(4x)+cos^2(4x))

\int (sin^{2} (4 x) + cos^{2} (4 x)) d x

x + C

Solution steps

\int sin^{2} (4 x) + cos^{2} (4 x) d x

Rewrite using trig identities

= \int 1 d x

Integral of a constant:

\int a d x = a x

= 1 \cdot x

Simplify

= x

Add a constant to the solution

= x + C

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\int 10 x sin (x) cos (x) d x

What is the integral of (sin^2(4x)+cos^2(4x)) ?
The integral of (sin^2(4x)+cos^2(4x)) is x+C