What is the integral of (x^2-5sin(x)+sec^2(x)) ?

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

Popular >

integral of (x^2-5sin(x)+sec^2(x))

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

\frac{x ^{3}}{3} + 5 cos (x) + tan (x) + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

\int 5 sin (x) d x = - 5 cos (x)

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

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

Simplify

= \frac{x ^{3}}{3} + 5 cos (x) + tan (x)

Add a constant to the solution

= \frac{x ^{3}}{3} + 5 cos (x) + tan (x) + C

\int (- 4 x^{6} + 6 x^{4} + 3 x^{3} + 6) d x

\int \frac{9}{x ln ( 4 x )} d x

\int \frac{3 + x}{3 - x} d x

\int (\frac{2 x}{x ^{2} + cos ( z )}) d x

\int 4 e^{8 x} d x

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