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Popular >

integral of 5xsec^2(x)

Solution

\int 5 x sec^{2} (x) d x

Solution

5 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 5 x sec^{2} (x) d x

Take the constant out:

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

= 5 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

: x tan (x) - \int tan (x) d x

= 5 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 5 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 5 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 5 (x tan (x) + ln ∣ cos (x) ∣) + C

Popular Examples

derivative of (x^2-2x-1/((x-1)^2))

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

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\int (- 8 cos (x) - 2 x) d x

integral of 1/(sqrt(16x^2-49))

\int \frac{1}{16 x ^{2} - 49} d x

integral of sin(8-x)

\int sin (8 - x) d x

integral from-1 to 0 of x^2

\int_{- 1}^{0} x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 5xsec^2(x) ?
The integral of 5xsec^2(x) is 5(xtan(x)+ln|cos(x)|)+C