What is the integral from 1 to 3x-1 of (f(t))/t ?

The integral from 1 to 3x-1 of (f(t))/t is 3xf-2f

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integral from 1 to 3x-1 of (f(t))/t

\int_{1}^{3 x - 1} \frac{f ( t )}{t} d t

3 x f - 2 f

Solution steps

\int_{1}^{3 x - 1} \frac{f t}{t} d t

Cancel the common factor:

t

= \int_{1}^{- 1 + 3 x} fd t

Integral of a constant:

\int a d x = a x

= [f t]_{1}^{- 1 + 3 x}

Compute the boundaries:

3 x f - 2 f

= 3 x f - 2 f

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\int_{- 3}^{0} \frac{1}{( x - 1 ) ^{2}} d x

\int_{- 6}^{3} - \frac{1}{x ^{4}} d x

\int_{0}^{2 π} 2 sin (θ) cos (θ) d θ

\int_{5}^{3} x^{2} d x

What is the integral from 1 to 3x-1 of (f(t))/t ?
The integral from 1 to 3x-1 of (f(t))/t is 3xf-2f