What is the integral of 5sin(3x)-4xsec(x^2) ?

The integral of 5sin(3x)-4xsec(x^2) is -5/3 cos(3x)-2ln|tan(x^2)+sec(x^2)|+C

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integral of 5sin(3x)-4xsec(x^2)

\int 5 sin (3 x) - 4 x sec (x^{2}) d x

- \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2}) + C

Solution steps

\int 5 sin (3 x) - 4 x sec (x^{2}) 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 5 sin (3 x) d x - \int 4 x sec (x^{2}) d x

\int 5 sin (3 x) d x = - \frac{5}{3} cos (3 x)

\int 4 x sec (x^{2}) d x = 2 ln tan (x^{2}) + sec (x^{2})

= - \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2})

Add a constant to the solution

= - \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2}) + C

\int \frac{x ^{2} + 1}{x ^{3} + 4 x ^{2} + 3 x} d x

\int w^{3} sin (w) d w

\int tan^{3} (3 x) sec^{6} (3 x) d x

\int \frac{1}{x 6 x - 1} d x

\int \frac{1}{x ^{2} - n} d x

What is the integral of 5sin(3x)-4xsec(x^2) ?
The integral of 5sin(3x)-4xsec(x^2) is -5/3 cos(3x)-2ln|tan(x^2)+sec(x^2)|+C