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

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integral of sin(x^2+1)

integral

sin (x^{2} + 1)

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

2 + 5 x

x (4 - x)^{\frac{1}{2}}

e^{1 - x}

\frac{r ^{2}}{( a ^{2} - r ^{2} )}

\frac{2}{( 1 - x ^{2} )}

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