What is the integral of 5t^4cos(t^5+1) ?

The integral of 5t^4cos(t^5+1) is sin(t^5+1)+C

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integral of 5t^4cos(t^5+1)

\int 5 t^{4} cos (t^{5} + 1) d t

sin (t^{5} + 1) + C

Solution steps

\int 5 t^{4} cos (t^{5} + 1) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int t^{4} cos (t^{5} + 1) d t

Apply u-substitution

: \int \frac{cos ( u )}{5} d u

= 5 \cdot \int \frac{cos ( u )}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 5 \cdot \frac{1}{5} sin (u)

Substitute back

u = t^{5} + 1

= 5 \cdot \frac{1}{5} sin (t^{5} + 1)

Simplify

5 \cdot \frac{1}{5} sin (t^{5} + 1) : sin (t^{5} + 1)

= sin (t^{5} + 1)

Add a constant to the solution

= sin (t^{5} + 1) + C

\int (csc^{2} (θ) - 1) d θ

\frac{d}{d x} (\frac{x 2 x + 1}{4 - 5 x})

\int \frac{4 - 3 x ^{2}}{( 3 x ^{2} + 4 ) ^{2}} d x

\int q^{2} cos (4 q) d q

3 x^{2} + 3 x - 5

What is the integral of 5t^4cos(t^5+1) ?
The integral of 5t^4cos(t^5+1) is sin(t^5+1)+C