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

The integral of xcos(x^2+1)+x/(x^2+1) is 1/2 sin(x^2+1)+1/2 ln|x^2+1|+C

Popular >

integral of xcos(x^2+1)+x/(x^2+1)

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

\frac{1}{2} sin (x^{2} + 1) + \frac{1}{2} ln x^{2} + 1 + C

Solution steps

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

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

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

= \frac{1}{2} sin (x^{2} + 1) + \frac{1}{2} ln x^{2} + 1

Add a constant to the solution

= \frac{1}{2} sin (x^{2} + 1) + \frac{1}{2} ln x^{2} + 1 + C

\int (5 x^{2} + 3 x - 2) lo g_{3} (x) d x

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

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

\int \frac{1}{x ( 9 x + 4 )} d x

\int \frac{( x ^{2} + 1 ) ^{3} ( x + 2 )}{x ^{5}} d x

What is the integral of xcos(x^2+1)+x/(x^2+1) ?
The integral of xcos(x^2+1)+x/(x^2+1) is 1/2 sin(x^2+1)+1/2 ln|x^2+1|+C