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## Homework Statement

evaluate the definite integral ∫(0 to 3) dx/sqrt(25+x^2)

## Homework Equations

## The Attempt at a Solution

I first used substitution and set x=5tanθ, and dx=5tanθsecθdθ

then i wrote the integral as 5∫ tanθsecθdθ/sqrt(25(1+tan^2(θ))

after some simplification i got

∫tanθsecθdθ/secθ = ∫tanθ =tanθsecθ

I then used θ=arctan(x/5) from the original x substitution and my final solution looked like this

tan(arctan(3/5))sec(arctan(3/5))-tan(arctan(0))sec(arctan(0))

It is incorrect, can anyone let me know where i might have done something incorrectly? Thanks