What is the integral of 4x+cosh(x) ?

The integral of 4x+cosh(x) is 2x^2+sinh(x)+C

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integral of 4x+cosh(x)

\int 4 x + cosh (x) d x

2 x^{2} + sinh (x) + C

Solution steps

\int 4 x + cosh (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x d x + \int cosh (x) d x

\int 4 x d x = 2 x^{2}

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

= 2 x^{2} + sinh (x)

Add a constant to the solution

= 2 x^{2} + sinh (x) + C

\int x (1 + y) d y

\int \frac{1}{y + 4} d y

\int \frac{( x )}{( 7 x ^{2} + 3 ) ^{5}} d x

\int (1 - 4 t^{2})^{\frac{3}{2}} d t

2 x sin^{2} (x) + 2 x cos^{2} (x)

What is the integral of 4x+cosh(x) ?
The integral of 4x+cosh(x) is 2x^2+sinh(x)+C