What is the integral from 0 to pi/4 of 5/(cos(x)) ?

The integral from 0 to pi/4 of 5/(cos(x)) is 5ln(1+sqrt(2))

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integral from 0 to pi/4 of 5/(cos(x))

\int_{0}^{\frac{π}{4}} \frac{5}{cos ( x )} d x

5 ln (1 + 2)

Solution steps

\int_{0}^{\frac{π}{4}} \frac{5}{cos ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{\frac{π}{4}} \frac{1}{cos ( x )} d x

Rewrite using trig identities

= 5 \cdot \int_{0}^{\frac{π}{4}} sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= 5 [ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2)

= 5 ln (1 + 2)

\int_{1}^{7} \frac{15}{x ^{2} + 5 x + 4} d x

\int_{1}^{2} - \frac{4}{x ^{2}} d x

\int_{0}^{4} (4 - 2 x) d x

\int_{1}^{3} \frac{1}{( x + 7 ) ^{2}} d x

\int_{4}^{14} (4 - x) (x - 14) d x

What is the integral from 0 to pi/4 of 5/(cos(x)) ?
The integral from 0 to pi/4 of 5/(cos(x)) is 5ln(1+sqrt(2))