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Popular >

integral of sinh(3x-1)

Solution

\int sinh (3 x - 1) d x

Solution

\frac{1}{3} cosh (3 x - 1) + C

Solution steps

\int sinh (3 x - 1) d x

Apply u-substitution

: \int sinh (u) \frac{1}{3} d u

= \int sinh (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sinh (u) d u

Use the common integral:

\int sinh (u) d u = cosh (u)

= \frac{1}{3} cosh (u)

Substitute back

u = 3 x - 1

= \frac{1}{3} cosh (3 x - 1)

Add a constant to the solution

= \frac{1}{3} cosh (3 x - 1) + C

Popular Examples

integral of cos^3(x/4)

\int cos^{3} (\frac{x}{4}) d x

integral of (3x^2-3y^2)

\int (3 x^{2} - 3 y^{2}) d y

integral of ((2x+1)(x-2))/x

\int \frac{( 2 x + 1 ) ( x - 2 )}{x} d x

integral of (uln^2(1+u^2))/(1+u^2)

\int \frac{u ln ^{2} ( 1 + u ^{2} )}{1 + u ^{2}} d u

integral of 5/(5t-9)

\int \frac{5}{5 t - 9} d t

Frequently Asked Questions (FAQ)

What is the integral of sinh(3x-1) ?
The integral of sinh(3x-1) is 1/3 cosh(3x-1)+C