What is the integral of sin(x^2+1) ?

The integral of sin(x^2+1) is sin(1)sqrt(pi/2)\C(sqrt(2/pi)x)+cos(1)sqrt(pi/2)\S(sqrt(2/pi)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x^2+1)

\int sin (x^{2} + 1) d x

sin (1) \frac{π}{2} C (\frac{2}{π} x) + cos (1) \frac{π}{2} § (\frac{2}{π} x) + C

Solution steps

\int sin (x^{2} + 1) d x

Rewrite using trig identities

= \int cos (x^{2}) sin (1) + cos (1) sin (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 cos (x^{2}) sin (1) d x + \int cos (1) sin (x^{2}) d x

\int cos (x^{2}) sin (1) d x = sin (1) \frac{π}{2} C (\frac{2}{π} x)

\int cos (1) sin (x^{2}) d x = cos (1) \frac{π}{2} § (\frac{2}{π} x)

= sin (1) \frac{π}{2} C (\frac{2}{π} x) + cos (1) \frac{π}{2} § (\frac{2}{π} x)

Add a constant to the solution

= sin (1) \frac{π}{2} C (\frac{2}{π} x) + cos (1) \frac{π}{2} § (\frac{2}{π} x) + C

\int_{- 2}^{4} (- x^{2} + 2 x + 8) d x

\frac{d y}{d x} = (sin^{2} (2 x)) (cos^{2} (y))

t \frac{d y}{d t} = t^{3} + 20 t^{3} y

\int 1.5 sin (- x + 2) d x

y = cos (x) - x sin (x)

What is the integral of sin(x^2+1) ?
The integral of sin(x^2+1) is sin(1)sqrt(pi/2)\C(sqrt(2/pi)x)+cos(1)sqrt(pi/2)\S(sqrt(2/pi)x)+C